The home side spurned two chances to extend their advantage before the break but Barca levelled in the 52nd minute when Luis Suarez glanced in Lionel Messi's free kick.
Sergio Busquets called on Barcelona to sign more players after the club's 3-1 Spanish Super Cup defeat by Real Madrid on Sunday.
Spanish media had reported that Xavi had been approached by Barca to replace Ernesto Valverde before Quique Setien was appointed in January.
Barcelona were held to a 1-1 draw at relegation-fighting Las Palmas on Thursday in an unexpected setback that left them with a five-point lead in La Liga ahead of their top-of-the-table showdown with Atletico Madrid this weekend.
Unzue is one of the two leading candidates to succeed Luis Enrique, who announced this month he will leave at the end of this season, along with Athletic Bilbao coach Ernesto Valverde.
Real Madrid were made to toil by the 10 men of Athletic Bilbao but eventually won 3-1 on Tuesday thanks to two strikes from Karim Benzema to go level on points with La Liga leaders Real Sociedad.
A round-up of Tuesday's action in the UEFA Champions League.
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.
Having won eight of the past 12 league titles coming into this campaign, where has it gone so wrong for Barcelona?
Athletic Bilbao's Spanish Super Cup victory against Barcelona not only earned them their first major trophy in 31 years but also ended coach Ernesto Valverde's long wait for silverware.
The draw means second-placed Atletico Madrid could close the 12-point gap with Barcelona, who are on 74 points, if they beat Celta Vigo later on Saturday.
News of all that's transpired on and off the football field
Valencia are expecting a counter-attacking team such as Real Madrid rather than a possession-hungry side like Barcelona when they host Paris St Germain in the Champions League on Tuesday, coach Ernesto Valverde said.
Barca feel familiar February blues as tiredness sets in
A 'winning culture' may be one of the most over used terms in modern football but Real Madrid and Carlo Ancelotti proved on Saturday, at Liverpool's expense, that there truly is meaning and value in the concept.
The only goal of the game came from a clever cross by Lionel Messi although Barca's captain was kept unusually quiet for the remainder, after being left with a bloodied face from a clash with United's Chris Smalling.
It is a scenario few could have foreseen after Real won a Liga and Champions League double last term and began this season so convincingly.
Barcelona's last Champions League triumph came in 2015, and since then they have failed to get beyond the quarter-finals while Real Madrid have monopolised the trophy.
Barca's Suarez in firing line after European away goals drought
Philippe Coutinho's versatility makes him a great acquisition for Barcelona, coach Ernesto Valverde said on Sunday as the Brazilian made his first public appearance at the Nou Camp following his 142-million-pound ($192.57-million) move from Liverpool.
Ousmane Dembele endured a rough start to his Barcelona career but the French winger appears to be finding his feet at a crucial time in the season.
The shock of the season saw Barca suffer their first league loss since going down 2-0 to Malaga on April 8, 2017, ending an incredible, record-breaking sequence that had lasted 43 games.
La Liga champions Barcelona's domestic struggles continued as they dropped points for the third game in a row, drawing 1-1 at home to Athletic Bilbao on Saturday after Lionel Messi and Sergio Busquets had begun the match on the substitutes' bench.
Messi opened the scoring at the Nou Camp with an audacious chipped penalty then restored control in the tie after Lyon had pulled a goal back to make it 2-1, hitting a decisive third goal after a trademark dazzling run to shake off four defenders.
'It has been good on pitch and off pitch,' Lampard said.
Real Madrid overcame an early howler from Sergio Ramos to beat Real Sociedad 3-1 at home on an eventful Saturday at the Santiago Bernabeu, where Gareth Bale was loudly booed by his own supporters and Luka Modric returned to his very best form.
Barcelona have one hand firmly on the La Liga title after winning 2-0 at Alaves on Tuesday, leaving them 12 points clear at the top of the table with four games to play.
Messi's damning assessment of the team came home to roost when the season re-started after the coronavirus stoppage and Barca surrendered the league title to Real Madrid, prompting the captain to launch a new tirade against the team.
Lionel Messi scored one penalty and missed another as Barcelona beat Real Valladolid 1-0 on Saturday to open up a seven-point lead at the top of La Liga.
Spanish media paid tribute to Barcelona captain Andres Iniesta after he starred in his side's 5-0 thrashing of Sevilla in the King's Cup final on Saturday.
Ousmane Dembele's late strike rescued a 1-1 draw for champions Barcelona at Atletico Madrid but Sevilla moved top with a 1-0 win over Real Valladolid. European champions Real Madrid were humiliated in a 3-0 defeat at Eibar.
La Liga leaders Barcelona beat Real Madrid 1-0 to all but knock their rivals out of the title race on Saturday, while second-placed Atletico Madrid stayed seven points behind the Catalans with a 2-0 win at Real Sociedad on Sunday.
News of all that's transpired on and off the football field
Barca play their final league La Liga game of the season at Alaves on Sunday before hosting Napoli on Aug. 8 in the second leg of their Champions League last-16 tie.
Barcelona opened up a four-point gap at the top of La Liga, maintaining their 100 percent start as they cruised to a 3-0 victory at Catalan rivals Girona on Saturday.
Barcelona captain Lionel Messi scored two goals and set up two more as the Catalans thrashed Real Valladolid 5-1 to move top of La Liga on Tuesday.
Barcelona have been haunted by their recent failures in the Champions League and there are concerning signs for the Catalans as they prepare for Tuesday's last-16 first leg away to Olympique Lyonnais.
Costa turned Juanfran's low cross into the net in the 69th minute for Atletico's third goal in the first leg of the last 16 tie against third division Lleida but immediately limped to the sidelines. He did return to the pitch, however, and completed the game despite bleeding from his knee.
Catalans will have to cope without their inspirational captain Andres Iniesta, the man who has pedigree when it comes to beating the Blues.
Champions Barcelona lost 2-0 at Celta Vigo while Getafe earned an important 2-0 win over Girona in their bid to secure Champions League qualification.
