However, they fought back to lead 3-2, before West Brom equalised to ensure that the match was level at the break.
A Christian Benteke penalty in the second half proved to be enough and Villa held on for a dramatic 4-3 win.
Here, Sports Mole takes a closer look at the 90 minutes to establish if it was a fair result.
On target: 6
West Bromwich Albion
On target: 4
Was the result fair?
This was a brilliant match, from the first minute to the last, with both teams playing some great football. However, they also defended abysmally, which explains the 4-3 scoreline. For the first 10 minutes West Brom had control, but they let Villa back in and paid for their lack of concentration. Despite equalising before the break, the Baggies failed to produce in the second half and Villa were the stronger outfit overall.
Aston Villa's performance
The home side had some early possession, but were stunned when Chris Brunt found the net with a sublime volley in the fourth minute. It got worse for Paul Lambert and his men moments later, but their response was first-class. They battled hard for the ball and made the most of their opportunities. Lambert will be delighted with the performance of Christian Benteke up front, who caused the West Brom defence numerous problems. However, he will be concerned by the lack of cohesion at the back and the manner of the Baggies' goals.
West Brom's performance
Pepe Mel will be an unhappy man tonight, but there were some elements of West Brom's performance that he can be pleased with. For example, they created chances and looked a threat going forward, and they scored three goals away from home. However, all of their good work was undone by horrendous defending. After going 2-0 up they should have tightened up at the back and played on the counter-attack, but instead they opened up.
Sports Mole's man of the match
Christian Benteke: The Villa striker was back to his best tonight and a constant threat throughout. He led from the front and was key to Villa's comeback. He deservedly got the winning goal from the penalty spot and is playing with confidence again.
This could be Fabian Delph's own goal in the first half, but he was trying to clear the ball and was unfortunate to see it hit the back of the net. Instead, this award goes to Diego Lugano, who missed a fantastic chance to give the Baggies the lead shortly after the break. He then pulled down Benteke to give away the crucial penalty.
Mark Clattenburg had a decent evening and got most of the big decisions correct. Morgan Amalfitano wanted a penalty shortly after coming on, but Clattenburg rightly waved play on. However, he had little choice but to award a spot kick when Lugano challenged Benteke.
Villa: Villa travel to Goodison Park to play Everton on Saturday.
West Brom: West Brom face a tough home match against Liverpool on Sunday afternoon.