Belgian Benteke, 22, enhanced his burgeoning reputation and took his season's tally to 18 league goals as Villa climbed to 16th place in the table on 37 points with three matches left, five ahead of third-bottom Wigan Athletic who have a game in hand.
Sunderland, who had Stephane Sessegnon sent off after 70 minutes, also have 37 points from 35 games following their second defeat under new manager Paolo Di Canio, level with north-east rivals Newcastle United who slipped below Villa on goal difference.
"The most important thing was to win the game," Villa manager Paul Lambert told Sky Sports. "The performance was absolutely outstanding. Benteke has been absolutely world class. He's a really humble guy and he can be anything he wants."
Villa captain Ron Vlaar broke the deadlock after 31 minutes, rifling a low shot from 30 yards into the corner of the net.
The home side's lead lasted less than a minute, however, as Sunderland defender Danny Rose played a neat one-two with Danny Graham before slotting a composed finish past Brad Guzan.
Villa regained the lead before half-time when Matthew Lowton's cross was calmly finished from 12 yards by forward Andreas Weimann.
Benteke grabbed his first after 55 minutes by heading in a rebound and he struck again with a firm header from Ashley Westwood's corner four minutes later.
After Sessegnon was sent off for a reckless tackle, the muscular striker completed his hat-trick with a cool angled finish and he gave Lambert a warm hug as he left the field following his substitution.
Gabriel Agbonlahor completed the rout two minutes from time.
"It was a very bad defeat and I am not very happy," Di Canio said. "Let us understand we have to play with desire and commitment every game. I have to make sure we are going to work hard to get the points we need to stay up.
"They [Villa] had a real desire and we have to make sure we get the points against Stoke now."
