Alan Pardew's side had gone over seven hours without a goal in the Premier League, but the France international struck in the 92nd-minute to lift the gloom hanging over Tyneside.
Remy had been Newcastle's biggest threat in the match, forcing Brad Guzan into several saves and hitting the post in the closing stages, before he had the final say.
Pardew had urged his players to prove Paul Lambert wrong after the Villa boss suggested Newcastle were there for the taking on the back of a sorry run that had seen them take just four points from the previous 24 available.
However, though Tim Krul was made to earn his clean sheet, Villa were ultimately undone.
Newcastle recalled Remy, Fabricio Coloccini and Cheick Tiote as they sought to avoid a defeat that would have consigned them to their worst home run since 1953, while Villa brought in fit-again forward Andreas Weimann and midfielder Karim El Ahmadi.
Pardew's message looked to have resonated with the team in the opening five minutes as the hosts managed to fashion a couple of decent chances.
First Remy struck a low drive straight at Guzan, before Cisse forced the American to parry a dipping curled shot from the edge of the box five minutes later.
The visitors gave the home crowd a scare four minutes later when Agbonlahor fired narrowly over from distance, before Bacuna stung the hands of Krul with a well-hit free-kick.
France striker Remy, who returned for the hosts after suspension, nearly found some luck with a set-piece of his own several minutes before the break, curling just wide of Guzan's left-hand post.
Cisse had not found the net at home since the Boxing Day win over Stoke City, but was handed a golden opportunity just before the break, courtesy of some great work from Remy.
The Frenchman dashed towards the byline before squaring to Cisse, who inexplicably fired over from six yards.
Substitute Yoan Gouffran wasted another decent opportunity by dragging a shot wide just after the break, before young full-back Paul Dummett sent a shot just over the bar from outside the area around 10 minutes later.
Newcastle threw on Luuk de Jong for the last 20 minutes, but it was Remy who looked the most likely source of a goal, bursting through the defence before forcing a great save from Guzan.
The hosts had a penalty shout late on when the ball appeared to strike Bacuna's arm, with referee Martin Atkinson waving away appeals as Newcastle grew frustrated.
De Jong nearly helped break the deadlock two minutes from time, squaring to Remy inside the six-yard box, only for the Frenchman to rattle an effort off the post.
But Remy made amends with a minute to play, lashing home from inside the area to hand the hosts a vital win and move them into eighth place in the table.
