Dwight Gayle punished Glenn Whelan's clumsy slip to put Albion into an early lead, but in the final 15 minutes a strike from substitute Conor Hourihane and a quickfire Tammy Abraham second from the spot turned the game on its head before Gayle saw red for a second caution.
West Brom finished four points better off than their opponents at the end of the regular season and they started the stronger at Villa Park, taking the lead in the 16th minute through Gayle's strike.
The on-loan striker made the most of some sloppy play from Whelan, charging through on goal and blasting past Jed Steer - who had earlier produced a fine save to keep out Jay Rodriguez's curler.
Villa struggled for attacking ideas in the first half but they looked a lot brighter in the second, coming close through a couple of Abraham attempts.
And the complexion of the tie completely changed in the space of four minutes as Hourihane sent a swerving shot past Sam Johnstone from outside the box and Abraham converted a spot-kick after Kieran Gibbs fouled Jack Grealish.
West Brom had a penalty shout of their own turned down as Mason Holgate took a tumble and, to make matters worse, lost Gayle for the remainder of the match and the second leg to leave Villa in control ahead of Tuesday's return at The Hawthorns.
