On loan Tottenham striker Jamie O'Hara's stunning strike looked to have settled the game in the first half.
But, with seconds remaining, Wolves keeper Wayne Hennessey spilled James Morrison's shot and Vela, who is on loan from Arsenal, converted the rebound.
Wolves had been the dominant force in the opening 45 minutes as they made the most of their numerical advantage in midfield.
O'Hara looked sharp and on his current form Wolves boss Mick McCarthy looks certain to take up the option to make the move from White Hart Lane permanent in the summer.
Matt Jarvis also caused problems down the left flank while Kevin Doyle was his usual threat as the lone striker.
It was a different story after the break as Wolves dropped deeper and Paul Scharner started to exert his influence in midfield.
O'Hara made a determined run at the Baggies defence inside the first 30 seconds before his eventual shot was blocked by Jonas Olsson.
A ball over the top of the Wolves back four from Gabriel Tamas almost played in top scorer Peter Odemwingie.
But Hennessey was alert to the danger and was able to clear from the edge of his area.
Matt Jarvis was causing problems down the left flank for Gonzalo Jara and another probing centre was headed over by O'Hara.
Hennessey was called upon to make the first save of the game after 21 minutes but he easily dealt with Olsson's header from Chris Brunt's corner.
West Brom started to gain a foothold in the game and Scharner's glancing header from a Nicky Shorey cross went just past the post.
Marc-Antoine Fortune should have done better when he headed a curling shot from Graham Dorrans over the bar from close range.
Then five minutes before half-time a stunning strike from O'Hara put Wolves ahead.
Doyle won a free-kick when he was brought down by Tamas 25 yards from goal.
Albion were caught napping when Milijas squared the free-kick to O'Hara and his curling shot flew past the dive of Myhill into the roof of the net.
It was the on loan Tottenham player's first goal for Wolves.
Wolves had the chance to double their lead with a 4-2 numerical advantage on the counter-attack.
But Doyle hesitated, when O'Hara was free to his left, and was crowded out.
Jarvis wasted a golden opportunity to double Wolves' lead after 51 minutes.
Tamas made a mess of trying to head the ball back to Hennessey and Jarvis nipped in with only the keeper to beat.
But, from 10 yards, out he dragged the shot wide of the far post.
In a rare Albion attack, Henry lost possession to Odemwingie who released the overlapping Fortune but his shot from a narrow angle was turned aside by Hennessey.
George Elokobi then made a great block to deny Odemwingie at close range and Scharner shot over from 12 yards out.
Wolves were dropping deeper and Fortune should have equalised after 63 minutes.
Odemwingie headed the ball across the box to Fortune but, from six yards out, he failed to make any contact on his attempted shot.
Jarvis atoned for his earlier miss when he headed a near post Olsson header off the line from Brunt's corner.
Albion striker Carlos Vela was soon involved in the action and Hennessey beat out his shot after he cut in from left.
Tamas was relieved when he turned Doyle's low centre inches wide of his own post at full stretch with Ebanks-Blake unmarked behind him.
Then, with seconds remaining, Vela equalised for Albion after Hennessey spilled James Morrison's low drive.