The 21-year-old Mexican striker, on loan from Arsenal, came off the bench to score his first goal for the Baggies to the delight of new manager Roy Hodgson, who was taking charge of West Brom for the first time since succeeding the sacked Roberto Di Matteo earlier this month.
The goal came after Wolves keeper Wayne Hennessey spilled a shot from substitute James Morrison, with Vela on hand to earn a vital point for the home side and deprive Wolves of a rare away success.
Wolves had looked to be heading off the bottom of the table with only their second away win of the season.
They went ahead against the run of play at The Hawthorns when Jamie O'Hara scored his first goal for Wolves since his loan move from Tottenham Hotspur. The midfielder ran onto Nenad Milijas's free-kick and curled the ball home from 22 metres out.
Wolves should have doubled their lead early in the second half, when a mistake by Gabriel Tamas allowed Matt Jarvis to break clear, but he fired wide of Boaz Myhill's goal with only the keeper to beat.
Tamas almost put through his own goal with eight minutes to play, but eventually West Brom did find the net - at the right end - to claim a point.
The result leaves Wolves bottom with 25 points from 27 matches, level with West Ham United and two points behind Wigan Athletic (27 from 27). West Brom stay one place and one point above the relegation zone on 28 points from their 27 games.
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