Luis Suarez twice put Barcelona in front at Balaidos with his first goals since January but Iago Aspas bent in a late free-kick to earn Celta Vigo a draw.
- Man Utd
Real Madrid and Barcelona are currently tied on 68 points but Zinedine Zidane's team leads the La Liga due to a superior head-to-head.
Real Madrid were held to a 2-2 draw by Celta Vigo thanks to a late goal by Santi Mina.
La Liga summed up Lionel Messi's performance using Amitabh Bachchan's iconic dialogue from Bollywood film Kalia.
Zinedine Zidane said he believes Gareth Bale will now stay, with the Spanish transfer window closing on September 2.
Eden Hazard, who injured his thigh in training on Friday, will certainly start when he is fit again and there will be much tougher opponents than Celta Vigo.
Lionel Messi, Luis Suarez and Philippe Coutinho were all among those left out ahead of the Champions League showdown against Liverpool at Anfield on Tuesday.
Real Madrid have taken maximum points from their opening 3 fixtures in contrast to the same point last season when they were already 5 behind Barcelona.
Gareth Bale pushed his case for a starting spot in the Champions League final vs Liverpool in Kiev in two weeks' time with two first-half strikes.
Barcelona's slip-up is a boost for Real Madrid and Atletico Madrid, who can close to within six points with victories over Athletic Bilbao and Real Sociedad respectively later on Saturday.
Real Madrid moved to within one point of winning La Liga as Cristiano Ronaldo struck twice to beat Celta Vigo 4-1
Marouane Fellaini's 17th-minute header put Manchester United 2-0 up on aggregate, but Celta Vigo hit back late on through Facundo Roncaglia, who was then sent off along with United's Eric Bailly following a centre-circle shoving contest.
Marcus Rashford's stunning free-kick 23 minutes from time put Manchester United on the brink of reaching the Europa League final with a hard-fought 1-0 win at Celta Vigo.
Leander Dendoncker struck late to snatch a 1-1 draw for Anderlecht against Manchester United in the first leg of Thursday's Europa League quarter-final, while crowd trouble overshadowed Lyon's tie with Besiktas.
Hampered by a series of injuries, Real Madrid's hopes of turning the tie around were dealt a huge blow when Danilo's own goal handed Celta Vigo to lead on the night just before half-time.
Real Madrid currently top La Liga with two wins from two games. They are still missing Cristiano Ronaldo due to the knee ligament injury that forced him off during Portugal's Euro 2016 final victory over France
Sevilla played out a 2-2 draw vs Celta Vigo which saw them win their Copa del Rey semi-final 6-2 on aggregate.
Lionel Messi is expecte to return for Barcelona's clash against Celta Vigo at the Camp Nou, where he needs only two goals to become the first player in the Spanish league to score 300 goals.