The Argentine marksman had been without a goal in five games across all competitions in 2015 since returning to action from a knee injury - and his fitness concerns resurfaced again at the Britannia Stadium.
City were also winless during that period, allowing Chelsea to open up a commanding seven-point lead in the title race, and the champions endured a torrid opening on Wednesday.
James Milner was fortunate to escape punishment for handling Peter Crouch's goalbound header before then setting up Aguero for a superb 33rd-minute opener.
Crouch levelled with his fifth career goal against the Manchester club five minutes later before Aguero was barracked by the home crowd having had a goal disallowed for handball in first-half stoppage time.
But, after Milner had restored Manchester City’s advantage, Aguero netted his 21st goal of the season from penalty spot.
Samir Nasri scored a brilliant fourth to secure the victory but by that stage Aguero had hobbled out of the action - while a late winner by Willian against Everton at Stamford Bridge preserved Chelsea's advantage.
Eliaquim Mangala and Aleksandar Kolarov were named in a revamped Manchester City defence while Crouch and Milner - included in their respective team's starting line-ups on the back of late weekend equalisers - were involved in an early flashpoint.
Joe Hart turned a stinging sixth-minute effort from Victor Moses behind and Crouch’s header from the resulting corner was blocked in the goalmouth by Milner, with television replays showing Stoke had a strong case in their appeals for handball.
Hart and the Manchester City backline were unconvincing during the opening exchanges and the England goalkeeper was spared by an offside flag in the 20th minute when he spilled Moses’ low cross for Crouch to convert.
A venomous drive from Steven N’Zonzi was parried by Hart and Moses smashed the rebound wide before Aguero took centre stage.
Collecting a long ball forward from Milner, the Argentinian grappled with Marc Muniesa on halfway and drove purposefully towards the Stoke box to clinically find the bottom corner.
Marko Arnautovic blasted a shot off target when Hart mishandled again from a corner but the Stoke attacker soon atoned for his error with a superb right-wing cross for Crouch to head the equaliser.
The opening 45 minutes ended in controversy as Aguero converted a David Silva cross from close range with a flick of his hand and was booked.
Stoke goalkeeper Asmir Begovic saved with his feet from Kolarov two minutes into a second half that Manuel Pellegrini's team began with far greater conviction.
They were rewarded when Milner planted home a fine 55th-minute header from Nasri's searching right-wing cross.
Moses curled a 68th-minute free-kick off target as Stoke looked to respond but their attacks were increasingly sporadic, and Aguero extended the visitors' lead from 12 yards after Geoff Cameron had brought down Silva.
Nasri stylishly sealed the points 14 minutes from time, running at a backpeddling Stoke defence to rifle in a 20-yard shot, leaving Manchester City to sweat on their talisman Aguero.
