Both goals came from corners in an entertaining first half as the rain poured down at the Ramon Sanchez-Pizjuan Stadium.
Jules Kounde was sent off for Sevilla after the break but, despite playing against 10 men for half an hour, Barca were unable to snatch the winner that would have seen them climb into the top four for the first time since August.
Instead, Xavi Hernandez's side move up to seventh, two points off a Champions League spot, while Sevilla missed the chance to move within three points of Real Madrid. They remain second, five points behind the leaders.
"We've dropped two points," Xavi said in his post-game news conference. "We deserved to win, even when it was 11 against 11, but I've seen a Barcelona with character and that's what I want. The team is growing.
"So, overall, it's a bittersweet feeling. I will struggle to sleep [because] we had to win, especially against 10. We must be calmer when we have the extra man, but I am proud of the team despite the result, which was the worst part of the game."
Sevilla grew into the game with Rafa Mir a threat. The striker had a goal ruled out for offside before firing off target from 20 yards.
Gomez eventually broke the deadlock in the 32nd minute for the home side. A clever corner routine ended with the Argentina forward finishing brilliantly from just inside the box.
Barca levelled just before half-time from a corner of their own, defender Araujo rising highest to power Ousmane Dembele's delivery into the corner.
Sevilla were the better side at the start of the second half, with Mir and Thomas Delaney both missing chances, but the momentum swung when Kounde was dismissed. The France defender reacted to a Jordi Alba by throwing the ball into the Barca player's face to earn a straight red.
Gavi headed a good chance over as Barca chased a winner, but it was Dembele who looked most likely to make something happen late on. The France international struck the woodwork with a fine individual effort before setting up substitute Luuk de Jong, playing against his parent club, only for the Dutch striker to head straight at Bounou.
There was still time for Jordi Alba to force a final save from Bounou in stoppage time, too, as both teams were forced to settle for a point.
We've taken a step forward. We played well against a difficult side in Sevilla. We deserved more because we were better in the second half. There were good spells in the first half, too, so it's a shame we switched off a little for their goal. We're on the right path," Araujo said after the match.
Xavi added: "We lacked some fortune. Ousmane [Dembele] hit the post, Gavi came close. The team competed, they're improving and pressing well. Barca are built to win games, but we're on the right path. This Barca is what I want."