Barca, who were without injured talisman Lionel Messi, started on the back foot and fell behind when Nabil Fekir netted with a sublime angled strike in the 15th minute. Griezmann, who joined Barca last month from rivals Atletico Madrid, scored four minutes before halftime to level the scores.
Simeone's side leapfrogged Real Sociedad into fourth on 42 points, while Sevilla stayed third in the standings on 46 after beating Las Palmas 1-0, also on Sunday, thanks to a late strike from substitute Joaquin Correa
Salzburg forced Lazio into a second-half capitulation as the Italians crashed out in the Europa League quarter-finals after losing 4-1 but Olympique de Marseille staged a thrilling fightback to see off visitors Leipzig 5-2 on Thursday. Arsenal also reached the semi-finals after recovering from a wobble to draw 2-2 at CSKA Moscow and progress 6-3 on aggregate, while favourites Atletico Madrid reached the last four after losing 1-0 at Sporting to go through 2-1 over the two legs.
Lionel Messi notched a 20th assist of the season to help a lacklustre Barcelona secure a 1-0 win away to Real Valladolid on Saturday, maintaining the pressure on La Liga leaders Real Madrid. Cristiano Ronaldo converted two penalties, both awarded for handballs and the second in the last minute, as Serie A leader Juventus twice hit back to draw 2-2 with Atalanta to move closer to a ninth successive Serie A title on Saturday.
Neymar struck twice as Barca beat Atletico Madrid to reach the King's Cup semis
Sevilla became surprise Liga leaders on Sunday after beating visiting Celta Viga 2-1 while champions Barcelona drew 1-1 at Valencia thanks to another Lionel Messi strike but are still without a victory in their last four league games.
Atletico Madrid knocked Barcelona off the top of La Liga, for a day at least, as a second-half strike by Koke earned a 1-0 victory over a stubborn Malaga side on Saturday.
Lionel Messi created a goal and scored another as Barcelona came from behind to beat struggling Rayo Vallecano 3-1 at home on Saturday and stay seven points clear at the top of La Liga.
Real Madrid's Gareth Bale came off the bench and coolly converted a controversial penalty to secure a 2-1 win at Levante in La Liga on Sunday as the European champions rode their luck to stay within nine points of leaders Barcelona.
When Barcelona host local rivals Espanyol on Saturday hoping to edge closer to the La Liga title, many may be haunted by Raul Tamudo's 89th minute equaliser which wrecked their title bid in 2006/07.
Lionel Messi was back in scoring business for Barcelona on Sunday, leading them to a resounding 4-0 win at home against Villarreal in a near-perfect La Liga opener for the Catalans under new coach Ronald Koeman.
Atletico Madrid must not let down their guard after Wednesday's thumping Champions League win at home to Malmo, coach Diego Simeone said.
Champions Barcelona begin their bid for a sixth La Liga title in eight years at Athletic Bilbao on Sunday knowing that fellow heavyweights Real Madrid could, unusually, be just one of several challengers for their crown.
Atletico Madrid captain Gabi said his team would not be lulled into complacency by Barcelona's faltering form when they host the Champions League holders in the second leg of their quarter-final on Wednesday.
Last season's treble winners Barca are in their worst run of form in La Liga since coach Luis Enrique took charge in August 2014.
Before Leicester enchanted the sporting world last year with their miraculous Premier League title win, Atletico had worked similar wonders in 2014 by breaking the strangehold of Real Madrid and Barcelona in La Liga.
Joao Miranda and new signing Mario Mandzukic led Atletico Madrid to a 2-1 home win in La Liga on Saturday as visitors Eibar were unable to cope with the aerial threat of the champions.
'But I want to be Giovanni and nothing more. It is not easy to live with his greatness. That's why I have to become stronger than him. I have to prove that, if I'm here, it's only because of me'
Atletico Madrid extended their dominance over neighbours Real with a 1-0 derby win on Saturday that leaves the Bernabeu team virtually out of the Liga title race.
Champions Barcelona moved five points clear at the top of La Liga with a 2-1 win at Getafe, while Real Madrid fell to a 2-0 defeat by Real Sociedad.
Real Madrid and Atletico each slipped 10 points behind La Liga leaders Barcelona after an intense Madrid derby finished goalless and the Catalans picked up an 11th victory in 12 games by winning 3-0 at Leganes.
Atletico Madrid striker Alvaro Morata scored a goal and then missed a penalty as his side began their La Liga campaign with an eventful and nervy 1-0 win at home to Getafe on Sunday which saw both teams reduced to 10 men.
Spanish teams have ruled with an iron fist in Europe for the last few years but a disappointing round of results in the Champions League has left the media wondering if this dominant era might be grinding to a halt.
After the reigning English Premier League champions suffered a shocking 0-1 defeat at home to Bournemouth on Saturday, will Jose Mourinho continue to lead the defending champions for the second half of the season? Here's a look the men who could take over at Stamford Bridge.
News of all that's transpired on and off the football field
A Marco Asensio-inspired Real Madrid crushed Eibar 3-0 to close the gap on La Liga leaders Barcelona to five points on Sunday, with Karim Benzema starting on the bench.
Atletico Madrid striker Antoine Griezmann struck twice as the Spanish side outclassed hapless Olympique de Marseille 3-0 on Wednesday to win the Europa League for the third time.
As soon as the final whistle confirmed Real Madrid's berth in the Champions League final against local rivals Atletico with a 1-0 aggregate victory over Manchester City on Wednesday, memories of 2014's all-Spanish final came flooding back.
Images from Wednesday's action in the UEFA Champions League.
Barcelona drew 1-1 at Valencia after Real Madrid lost 1-0 away to Alaves, allowing Sevilla to go top of La Liga with a 2-1 home win over Celta Vigo on Sunday. Here are five talking points from the weekend's La Liga action.
Alvaro Morata again proved decisive from the bench by striking a late winner against Athletic Bilbao and firing a lacklustre Real Madrid to the top of La Liga on Sunday. The Spain international has been afforded limited opportunities in his first season back at Real following two years with Juventus, struggling to usurp first choice forwards Gareth Bale, Cristiano Ronaldo and Karim Benzema. Morata has made just four league starts, but has scored four times in all competitions.
La Liga's reputation as the epicenter of world soccer talent has been bruised by the world record smashing sale of Neymar to Paris St Germain and how Barcelona react to the departure of one of their leading players will define the new season in Spain.
Atletico Madrid kept pace with leaders Barcelona and restored their five-point lead over third-placed city rivals Real when Diego Costa and David Villa each scored a penalty in a 2-1 win at Granada in La Liga on Thursday.
Atletico Madrid's problems deepened as they were held to a 0-0 draw at Villarreal in La Liga on Friday, stretching their winless run to four games in all competitions.
IMAGES from the Europa League matches played on Thursday
Diego Costa gave Europa League holders Atletico a dream start against Champions League winners Real by firing them ahead after 49 seconds, knocking down a long pass and smashing the ball into the net from a tight angle.
Karim Benzema fired Real Madrid to a 1-0 win in the city derby against Atletico Madrid on Saturday which underlined Real's La Liga title credentials. Bayern Munich scored three goals in the opening 26 minutes to defeat Mainz 05 3-1 away on Saturday and go two points clear at the top of the Bundesliga with their sixth straight win.
Images from the football matches played across Europe on Sunday.
Thomas Partey scored his first goal for Atletico Madrid as they reached the last 16 of the King's Cup with a 1-0 home victory over third-tier Reus on Thursday that secured a 3-1 aggregate success.
Antoine Griezmann had plenty of painful memories to erase in Thursday's European Championship semi-final against Germany and he did that in style, scoring twice to lead the host nation to an historic 2-0 victory over the world champions.