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Hodgson was moments away from opening his reign at the Hawthorns in the worst possible manner as Albion trailed to Jamie O'Hara's first goal for Wolves.
But Vela, on loan from Arsenal, spared Hodgson's blushes with a stoppage time equaliser which kept fourth bottom Albion outside the relegation zone and three points ahead of bottom club Wolves.
Former Liverpool boss Hodgson, appointed after Roberto Di Matteo's sacking, made one enforced change as midfielder Youssouf Mulumbu was ruled out with a hamstring injury, leading to a recalle for Gabriel Tamas.
Wolves had an early chance when O'Hara made a determined run at the Baggies defence inside the first 30 seconds, only for the on-loan Tottenham midfielder's shot to be blocked by Jonas Olsson.
Peter Odemwingie almost got clear when he ran onto Tamas's throughball but Albion's top scorer was denied as Wolves goalkeeper Wayne Hennessey cleared from the edge of the area.
Matt Jarvis was causing problems down the left flank for Gonzalo Jara and another probing centre was headed over by O'Hara.
Paul Scharner's glancing header from a Nicky Shorey cross went just past the post, then Marc-Antoine Fortune should have done better when he headed a curling shot from Graham Dorrans over the bar from close range.
Just as Hodgson's side were starting to take control, O'Hara put Wolves ahead with a fabulous strike.
Nenad Milijas squared a free-kick to O'Hara and his curling shot flashed past Boaz Myhill's despairing dive into the roof of the net.
Jarvis wasted a glorious opportunity to double Wolves' lead after 51 minutes.
Tamas made a mess of trying to head the ball back to Myhill and Jarvis nipped in with only the keeper to beat. But from 10 yards out he dragged the shot wide of the far post.
Albion pressed hard for an equaliser after that narrow escape and Odemwingie released Fortune but his shot from a narrow angle was turned aside by Hennessey.
Hodgson's side should have equalised after 63 minutes when Odemwingie headed the ball across the box to Fortune. However the former Celtic striker failed to make any contact as he missed his kick from close range.
Another chance came and went for Albion when Jarvis headed a near post Olsson header off the line from Chris Brunt's corner.
Hodgson sent on Vela in place of Dorrans soon after and his change almost paid off immediately as Hennessey beat out the forward's shot after he cut in from the left.
Vela always looked dangerous and, with seconds remaining, he was perfectly placed to equalise after Hennessey spilled James Morrison's low drive.
