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On the quarter-hour mark, Gabriel Agbonlahor got the ball into the back of the Magpies net, but the goal was ruled out for offside.
Benteke continued to create good chances for Villa, firing wide half an hour in before launching into an overhead kick that Tim Krul had to palm away moments later.
Despite the visitors' dominance, it was Newcastle that took the lead 37 minutes in when a Janmaat cross from the right was missed by the Villa defence, with Cisse controlling the ball and slotting into the net.
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After the restart Cisse was gifted a free header from Ameobi's free kick, but the effort flashed a couple of yards wide of Brad Guzan's goal.
Massadio Haidara was then forced to leave the field on a stretcher following an injury, with Ryan Taylor replacing him, and moments later, Tom Cleverley forced a save from Krul after pouncing on a Benteke flick-on.
Benteke continued to be a thorn in Newcastle's side as he fired a shot from a corner that needed a Fabricio Coloccini block to keep out, before bundling the ball into the back of the net from Ashley Westwood's low ball - only for the referee to disallow the goal for offside.
Follow that near-setback, the Magpies resumed their attack on Villa's goalmouth, with Taylor's kick forcing a save by Guzan and Ayoze Perez heading against the outside of the post.
Villa, meanwhile, have now suffered seven straight defeats and remain second from bottom.