Tomas Rosicky scored in each half before Arsenal survived the 70th-minute sending off of Per Mertesacker, which resulted in James Morrison's converted penalty, to climb provisionally into fourth place above Chelsea and just a point behind north London rival Tottenham.
It was the visitors' third straight league win — and sixth in their last seven matches — as they look to qualify for Europe's top competition for the 16th season in a row under manager Arsene Wenger.
"The team is growing from game to game and they showed it again today," Wenger said.
Villa scored twice in the last three minutes — including a stunning volley from 35 yards (meters) by Matthew Lowton — to beat stuttering Stoke 3-1 away and jump three points clear of the bottom three.
"I don't think you will see a better goal in Europe let alone anywhere else," Villa manager Paul Lambert said. "The technique, chest control and volley was outstanding."
Last-place Reading looks doomed, though, after losing 2-0 at home to Southampton to stay seven points adrift of safety with six games left. No team in the Premier League's 21-year history has survived facing such a deficit at this stage.
Southampton took a giant stride to safety, unlike Norwich, which conceded a 75th-minute equalizer to Luke Moore to draw 2-2 with Swansea and remain in relegation danger.
With Tottenham and Chelsea not playing until Sunday, Arsenal put pressure on its rivals from the capital to copy its wonderful form over the past month.
The 2-0 win at Bayern Munich on March 13 may not have kept the team in the Champions League but it appears to have done wonders for the confidence of Wenger's players for the Premier League run-in.
And just like last season, Rosicky has come good in spring, with the playmaker opening the scoring in the 20th by heading in from close range after good work by the rejuvenated Gervinho.
It was his first goal of the season and Rosicky made it 2-0 in the 50th by drilling a volley into the corner after his original shot was batted down by West Brom goalkeeper Ben Foster.
Center back Mertesacker ensured a nervy finish by getting himself red-carded for pulling down Shane Long. Morrison scored from the spot but heavy pressure from the hosts failed to deliver an equalizer.
"It was very difficult in the end and we had to show another aspect of our strength at the moment — resolve, spirit and fighting attitude," Wenger said.
Stoke, winless in six matches, was booed off at Britannia Stadium but it was all smiles with Villa, which took the lead through Gabriel Agbonlahor in the ninth minute.
Michael Kightly equalized in the 80th before Lowton's thunderbolt and Benteke's 15th of the campaign sealed Villa's third victory in four.
"We need a point a game and it is important the lads stay confident," Stoke manager Tony Pulis said. "We have (Manchester) United, Tottenham, Norwich at home and then tough games away from home, too. It is a good test for everyone at the football club now."
Well-crafted goals by Jay Rodriguez and Adam Lallana were enough to lift Southampton seven points clear of the bottom three and leave Reading with a near-impossible task to stay up.
"It's a situation we don't want to be in, but we're in it," said Reading manager Nigel Adkins, who had been looking for revenge against the club that fired him 78 days ago. "You can hide away or you can face up to the reality of it."
Norwich looked like earning a vital win to climb seven points clear of the bottom three after reacting to Michu's 35th-minute opener for Swansea with goals from Robert Snodgrass and Michael Turner either side of halftime.
However, Moore struck in the 75th and Norwich is five points ahead of third-from-bottom Wigan, which has played two games fewer.