WATCH LaLiga LIVE & EXCLUSIVE on beIN SPORTS | available via Foxtel, Kayo Sports, Fetch TV &CONNECT

Barca led twice but were pegged back on both occasions, Celta grabbing an 88th-minute equaliser through captain Iago Aspas's superb free-kick.

Suarez scored both goals for the visitors, ending a personal drought that stretched back to early January before he suffered a knee injury, but was left frustrated by the team's failure to see out the win.

While Quique Setien's side moved back top of the table courtesy of the point picked up on its travels, Real Madrid has the chance to leapfrog over it again if it avoids defeat at rock-bottom Espanyol on Monday (AEST).

Zinedine Zidane's side also holds the head-to-head advantage over the reigning champion, having picked up four points from the two Clasico meetings in 2019-2020.

"It was a vital match to fight for the title," Suarez admitted in his post-match interview.

"We had a good first half, creating chances, but in the second half it was different, Celta wanting to be more aggressive.

"It [the result] leaves a bitter taste, one of sadness and frustration because we have lost two points."

Lionel Messi set up both goals for Suarez, the first of which saw him head in a clever free-kick from close range after Celta had put players on the line to protect against a direct shot.

The Uruguayan striker found the net again in the 67th minute after Fedor Smolov's leveller earlier in the second half, albeit his brace was not enough.

Barca, which next faces Atletico Madrid on Wednesday (AEST), has now won just once in its past four away games in the league.

"For my part, I am happy to help with both goals, but you are angry because things have to be corrected," Suarez added.

"This was a complicated away game, as will be the trip to Villarreal. Then, in between, we host Atletico."