Villa had lost six consecutive away games and scored just four times on their travels in the top flight ahead of their trip to Wearside, but they ran riot against sorry Sunderland on Saturday.
Strike duo Benteke and Agbonlahor helped themselves to two goals apiece in the first half as Tim Sherwood masterminded a third straight victory.
Three points for Villa moved them two points above Sunderland in the table - and, on the evidence of this display, the FA Cup semi-finalists should stay out of trouble.
Sunderland, on the other hand, will be looking anxiously over their shoulders after an alarming display that prompted many fans to flock out of the ground before half-time.
Poyet's side have scored only one goal in their last five games and some supporters approached the dugout to vent their fury at the under-pressure head coach after they were swept aside in the first half.
After being devoid of an attacking threat for much of the season under Paul Lambert, Villa looked lively going forward from the off and they were two goals up after only 18 minutes.
First the lively Charles N'Zogbia set Leandro Bacuna away down the right with a clever first-time flick and he kept his composure to pick out the returning Benteke, who drifted away from his marker and side-footed calmly past Costel Pantilimon from just inside the penalty area.
Villa sensed Sunderland were there for the taking and took advantage of some poor defending from John O'Shea to double their lead less than two minutes later.
Ciaran Clark's ball down the line should have been dealt with by O'Shea, but he hesitated and Agbonlahor pounced to slide the ball under a stranded Pantilimon and inside the near post.
Scott Sinclair ought to have made furious Sunderland fans even more disgruntled when he somehow fired over the crossbar from five yards out after Bacuna had again got away down the right.
It came as no surprise when the third goal came eight minutes before half-time, though, and again it was all too easy for Agbonlahor.
The forward was allowed to cut in from the right and dribble inside the penalty area unchallenged before guiding a left-foot finish inside the far post to spark a mass exodus from the home supporters.
Angry fans were led away as they left Poyet in no uncertain terms about their feelings, and worse was to come when Benteke rose to head home Bacuna's cross and give Villa a four-goal just before the break.
Sunderland played for over three minutes with 10 men at the start of the second half before Sebastian Larsson eventually emerged from the tunnel and returned to the fray limping, during which time Pantilimon palmed over N'Zogbia's measured strike.
Steven Fletcher, making his first Premier League start since January, hit the post with just under 10 minutes left in a rare Sunderland attack, but picked up an injury in the process.
Sherwood then gave a debut to 16-year-old striker Rushian Hepburn-Murphy eight minutes from time as Villa coasted to victory and Sunderland were left shell-shocked.
