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.
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.