Arsenal manager Mikel Arteta continues rebuilding the side around goal machine Pierre-Emerick Aubameyang and younger talents like Bukayo Saka.
Lacazette fired the Gunners ahead in the eighth minute after poor defending by the home side before new signing Gabriel made it 2-0 in the 49th and Aubameyang put the icing on the cake with a superb shot into the top corner.
Arsenal's Pierre-Emerick Aubameyang struck a vital late goal to seal a 3-1 win over Valencia on Thursday and give his side breathing space for the second leg of their Europa League semi-final in Spain next week.
Tottenham Hotspur climbed to third with a 3-1 win over Southampton while Chelsea hung on to fourth spot, above Arsenal on goal difference, despite a 2-1 defeat at Wolverhampton Wanderers.
Liverpool took over at the top of the Premier League table despite being held to a 0-0 draw against Manchester United in a scrappy match on Sunday.
Manchester City are top on goal difference, with Chelsea second and Liverpool dropping to third, two points ahead of Arsenal, who routed Fulham 5-1.
Olivier Giroud scored the decisive spot kick as Arsenal beat Chelsea 4-1 in a penalty shootout to win the Community Shield at Wembley on Sunday.
Images from Sunday's action in the Premier League.
Reigning champions Manchester City took the lead after 24 seconds but suffered a shock 2-1 defeat at Newcastle United.
Liverpool and champions Manchester City drew 0-0 at Anfield while Chelsea and Arsenal enjoyed comfortable away wins. City are top on goal difference from Liverpool and Chelsea with Arsenal two points behind.
Arsenal will re-open their London Colney training ground to their players next week for individual training but the Premier League club will continue to observe social distancing rules amid the coronavirus outbreak, they said on Saturday. Soccer in England was suspended indefinitely last month due to the virus and no clubs have been in training.
IMAGES from EPL matches played on Saturday.
Sergi Canos and Christian Norgaard scored midway through each half to spark wild celebrations by the home fans who have waited so long to take their place in their new 17,500-capacity home and even longer to watch top-flight football.
Atletico Madrid substitute goalkeeper Antonio Adan saved three penalties before blasting home the winning spot-kick as the Europa League champions edged out Arsenal after the sides drew 1-1 in their International Champions Cup opener in Singapore on Thursday.
Chelsea beat Sheffield United 2-0 to reach the FA Cup semi-finals for the fourth time in five seasons.
West Brom, relegated from the Premier League last season, made 11 changes from the side that won at the weekend in the Championship and had five players -- including goalkeeper Alex Palmer -- making their debuts.
Arsenal fielded a strong team with Ozil installed as captain and the Premier League side soon took control against weakened opposition, given the time and space they will not be afforded when the domestic campaign kicks off in August.
Leicester City's Kelechi Iheanacho scored two poacher's goals as they beat Manchester United 3-1 in their FA Cup quarter-final on Sunday to set up a last-four clash against Southampton.
Daniel Ceballos fired Arsenal into the FA Cup semi-finals with a stoppage-time goal that sealed a 2-1 win over Sheffield United
Manchester United climbed two places up to second in the Premier League after Marcus Rashford scored deep into stoppage time to give them a fortuitous 1-0 home win over Wolverhampton Wanderers on Tuesday.
The Arsenal manager says money and 'starification' has become too important in football.
Chelsea's 0-0 home draw with second-placed United ensured Thomas Tuchel is still undefeated in nine games since replacing Frank Lampard, but it meant they failed to dislodge fourth-placed West Ham United who became Manchester City's 20th successive victims in all competitions on Saturday.
Timo Werner scored his first goal of the season as a much-changed Chelsea side crept into the fourth round of the League Cup by beating Aston Villa 4-3 on penalties after the Stamford Bridge clash ended 1-1 on Wednesday.
Hazard extra-time goal sends 10-man Real Madrid through to Copa del Rey final.
Europa League favourites Manchester United secured a 1-1 draw on a threadbare pitch at Rostov, while Olympique Lyonnais beat AS Roma 4-2 helped by a fine individual goal from Nabil Fekir in their last 16, first leg ties on Thursday.
Arsenal substitute Pierre-Emerick Aubameyang scored twice in three minutes and captain Mesut Ozil played a starring role as they extended their winning run with a 3-1 victory over Leicester City in the Premier League on Monday.
The brilliance of Chelsea's Eden Hazard ended Liverpool's 100 percent start to the season as Maurizio Sarri's side enjoyed a 2-1 win at Anfield in the League Cup third round on Wednesday.
Manchester United's troubled season hit a new low on Saturday as Jose Mourinho saw his gamble on introducing a new tactical system backfire with an insipid 3-1 defeat to West Ham United in the Premier League.
IMAGES from the English Premier League matches played on Sunday
Images from the Premier League matches played on Sunday.
The result leaves Arsenal in fifth place on 15 points, two behind Leicester City and Chelsea, while Sheffield United moved into ninth on 12 points.
The two previous meetings at Anfield ended in 4-0 and 3-1 defeats for Arsene Wenger's Arsenal teams, but there is a fresh optimism around the club after a successful transfer window.
The hosts struggled to break down Arsene Wenger's side despite enjoying the majority of possession and will feel hard done by after crafting the best of the game's few openings in a lively game at Stamford Bridge.
A dreadful defensive error from Arsenal's Granit Xhaka gifted Burnley an equaliser as the sides drew 1-1 at Turf Moor in the Premier League on Saturday.
Alexandre Lacazette's free-kick sent Arsenal into the Europa League semi-finals with a comfortable 1-0 win away over Napoli, while Chelsea beat Slavia Prague 4-3 in a roller-coaster game, helped by a Pedro brace.
Antonio Valencia's early thunderbolt put Manchester United en route to a 4-0 Premier League victory over Everton on Sunday, but they needed a flurry of late goals to finally subdue their unfortunate visitors.
Premier League champions Liverpool maintained their 100 per cent start to the season with a 3-1 win against Arsenal at Anfield on Monday leaving them level on nine points with pacesetters Everton and Leicester City.
Arsenal had to come from behind twice to beat Leicester City 4-3 in a thriller as the English Premier League season got off to a flying start on Friday with Arsene Wenger's substitutions turning the match around at The Emirates.
Two goals each for Roberto Firmino and Sadio Mane helped Liverpool to keep in touch with Premier League leaders Manchester City with a 4-2 win over lowly Burnley at Anfield on Sunday.
Chelsea moved within two points of fourth-placed Tottenham Hotspur in the Premier League after a 1-0 victory over Liverpool thanks to an Olivier Giroud header at Stamford Bridge on Sunday.
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