Villa offered dogged resistance, but Toure broke the deadlock with a characteristically languid strike in the 82nd minute and Aguero lashed home a second six minutes later.
Victory takes Manuel Pellegrini’s side to within two points of leaders Chelsea, who host Arsenal on Sunday.
“When we have just eight minutes to go you are a little worried, but I trusted that one of those chances would be scored because we have important players to do that,” Pellegrini told Sky Sports.
“It is very difficult to recover the points against a team like Chelsea and the only way to do it is to win every game.”
With Eliaquim Mangala back in the team, defending champions City bossed proceedings in the first half at Villa Park without ever truly exposing their hosts.
Aguero hit the post from James Milner’s pass early in the second period, but Villa quickly counter-attacked and City goalkeeper Joe Hart had to save from Kieran Richardson.
Belgian striker Christian Benteke made his return for Villa as a substitute after six months on the sidelines with a ruptured Achilles tendon, but it was City who dominated the closing stages.
David Silva prodded wide and Villa goalkeeper Brad Guzan saved from Aguero, Mangala and Frank Lampard, before Toure made the breakthrough with a curling left-foot shot from the edge of the box.
Aguero made the points safe in the 88th minute, gathering a pass from Milner and crashing a shot inside the right-hand post.
Earlier, Adam Lallana opened his Liverpool account in style as his side claimed a first win in four league games by edging West Bromwich Albion 2-1.
Lallana put Liverpool ahead in the 45th minute at Anfield with his first goal since signing from Southampton.
After wriggling away from three defenders, the England midfielder poked the ball to Jordan Henderson, whose clever back-heel freed Lallana to arrow a left-foot drive into the bottom-right corner.
Saido Berahino equalised with a 56th-minute penalty after Dejan Lovren was penalised for a foul on the West Brom striker that appeared to take place just outside the area.
But five minutes later, Raheem Sterling teed up Henderson to score the decisive goal with a low, first-time shot past England colleague Ben Foster.
– Cisse spares Newcastle –
“It was very satisfying. We had to show big character today,” said Liverpool manager Brendan Rodgers, who awarded a first league start to Rickie Lambert in place of Mario Balotelli.
“I thought the resilience of the players was fantastic and we were helped by the crowd, because they realised the team needed a lift. It was a big win for us.”
Henderson’s strike enabled Liverpool to bounce back from their mid-week defeat by Basel in the Champions League and saw them provisionally climb to sixth place in the table.
Senegalese striker Papiss Cisse prevented Newcastle United from slipping to a third consecutive away defeat by scoring a brace as his side twice hit back to draw 2-2 at Swansea City.
Swansea midfielder Gylfi Sigurdsson set up goals for Wilfried Bony and Wayne Routledge early in each half, but Cisse replied on each occasion to buy beleaguered Newcastle manager Alan Pardew some breathing space.
“It showed great spirit and character,” said Pardew, whose side remain without a league win.
“There’s always pressure when you’re behind in a game, but it’s my job to try and lift the players and make sure there’s fight in their belly.”
Recalled striker Steven Fletcher scored his first goals of 2014 as Sunderland belatedly registered their first win of the campaign with a 3-1 victory at home to Stoke City.
Connor Wickham’s fourth-minute header for Sunderland was cancelled out by Charlie Adam’s low strike in the 15th minute, but Fletcher struck either side of half-time to send Gus Poyet’s side up to 11th place.
Substitute Ross Wallace scored a dramatic 96th-minute free-kick to earn Burnley a 2-2 draw at fellow promoted side Leicester City.
Algerian winger Riyad Mahrez set up Jeffrey Schlupp to put Leicester ahead and then restored the hosts’ lead after Michael Kightly had equalised in the 39th minute, but Wallace curled home an equaliser deep into stoppage time.
Meanwhile, second-half goals by Mohamed Diame and Nikica Jelavic gave Hull City a 2-0 success at home to Crystal Palace.
In Sunday’s other games, third-place Southampton visit Tottenham Hotspur, Manchester United host Everton and West Ham United tackle Queens Park Rangers.