Dwight Gayle punished Glenn Whelan's clumsy slip to put Albion into an early lead, but in the final 15 minutes a blistering strike from substitute Conor Hourihane and a quick-fire second by Tammy Abraham 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 its opponent at the end of the regular season and started the stronger at Villa Park, taking the lead in the 16th minute through Gayle's strike.
The on-loan Newcastle United 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 looked a lot brighter in the second, coming close through a couple of Abraham attempts.
The complexion of the tie then 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 its 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 Wednesday's (AEST) return at The Hawthorns.