Two superbly-taken goals by Danny Welbeck and Solly March earned Albion their first ever win at Villa Park.
Welbeck produced a sumptuous finish to score his first Albion goal early on before March's precise finish restored their lead after Ezri Konsa equalised just after the break.
In a dramatic finale, Tariq Lamptey was sent off after collecting two yellow cards in quick succession and Albion got a break in stoppage time when referee Michael Oliver awarded a penalty for a foul by March, only to change his mind after checking VAR.
Head coach Graham Potter will regard that incident as a long overdue bit of good fortune for his side, who as well as scoring twice also created other chances and defended courageously when Villa pushed forward in the closing stages.
Villa suffered a blow within a minute when Ross Barkley tweaked his hamstring taking a free kick and had to be replaced.
Both sides were on the front foot from the start which made the first half a terrific watch.
Adam Lallana bravely blocked Trezeguet's shot before the Albion midfielder was heavily involved at the other end in Albion's 12th-minute opener.
The 32-year-old found Welbeck running from inside his own half onto a perfectly-weighted pass. Welbeck charged into the box and as Emiliano Martinez came out, he chipped the Villa keeper into an empty net.
The former Manchester United and Arsenal forward could have had a second four minutes later. Tariq Lamptey intercepted John McGinn's pass and played a great ball inside but Welbeck tried to take the shot on his right, giving Martinez enough time to come out and smother the ball.
Villa were stung into a response and Adam Webster brilliantly blocked Trezeguet's shot. The rebound fell to the Egyptian but he somehow blazed over from six yards when he should have scored.
Maty Ryan made three good saves before the break, pushing Bertrand Traore's shot round the left-hand post, clawing away Jack Grealish's effort before pulling off an unconventional stop to deny Tyrone Mings by volleying the ball to safety with his left before colliding with the upright.
But Albion had their moments too when they could have extended their lead before the break. Welbeck's weighted ball put Neal Maupay in, but Martinez blocked bravely and Lallana got his angles wrong trying to guide Lamptey's pass inside the post.
A breathless first half ended with Ben White getting across to deny Ollie Watkins with a great challenge just when the Villa striker was about to pull the trigger.
Joel Veltman replaced Lallana at the break with White moving into midfield but Albion were pegged back within two minutes of the re-start. Traore whipped in a free kick from the left and Konsa arrived unmarked at the far post to slide the ball inside the post with Ryan helpless.
The response, though, was excellent. In the 55th minute Albion broke down the left, Gross picked out March with a great pass and the winger took aim with his right foot 12 yards out and guided his shot deliciously into the top right-hand corner to make it 2-1.
Welbeck had a good chance to score his second after untidy Villa defending. Maupay's back-heel was blocked by a defender but Welbeck volleyed wide from an inviting position. The Frenchman made way for Dan Burn with ten minutes left with Albion content to soak up pressure and hit Villa on the break.
There was still drama to come. Lamptey, who had just been booked, picked up a second yellow for a foul on Grealish and then in stoppage time March was adjudged to have brought down Trezeguet. VAR disagreed and after checking the monitor referee Oliver changed his mind and moments later Albion could celebrate a precious three points.
Another Villa thriller for Danny
Albion have never won in B6 and haven't beaten them since 1980, but striker Danny Welbeck certainly isn't burdened by the weight of history against Villa. His goal was his fourth in his last three games at Villa Park for three different clubs following two goals for Manchester United there in 2013 and another for Arsenal a year later.
One Sunday newspaper reporter tweeted that Jack Grealish was Man of the Match before kick-off, but Albion will be pleased with how they coped with the threats from Villa's talisman who, after his England exertions, faded in the second half. Instead, Tariq Lamptey produced another eye-catching display, so much so that Grealish switched from the left-hand side to the right before occupying a more central role in the second half, leaving others to deal with the elusive Lamptey.
Gross delivers again
Pascal Gross is the king of assists for Albion. His precise pull-back, which Solly March finished with such aplomb, means he has now been involved in more Premier League goals than any Albion player with 17 assists and 12 goals. His 29 is one more than Glenn Murray (26 goals, 2 assists). March has now scored twice in six games, having scored his previous two goals in 92 appearances.
Ryan, Lamptey, White, Dunk, Webster, March, Bissouma, Gross (Molumby 90), Lallana (Veltman 45), Maupay (Burn 80), Welbeck.
Subs not used: Steele, Connolly, Jahanbakhsh, Alzate.
Referee: Michael Oliver