The Argentinian has been in blistering form in recent weeks, his brace in Wednesday's 4-1 demolition of Sunderland taking his tally for the season to 19 goals in all competitions.
But the City striker lasted just seven minutes at the Etihad Stadium on Saturday before hobbling off, to be replaced by Jose Angel Pozo.
After losing their talisman, another of City's key players stood up to be counted as Yaya Toure tucked away a first-half penalty to earn the champions their fifth consecutive victory in all competitions, capitalising on Chelsea's 2-1 defeat at Newcastle United earlier in the day.
Everton, who were denied a late equaliser when Joe Hart produced a stunning save to keep out Romelu Lukaku, have taken just one point from their past three league games as their inconsistent domestic form continues.
While City will undoubtedly be thrilled with another win, the injury to Aguero will cause major concern, especially with a crucial UEFA Champions League clash at Roma to come on Wednesday.
Everton boss Roberto Martinez brought in Samuel Eto'o for Ross Barkley and Tony Hibbert for Leon Osman - perhaps with an eye on having extra defensive cover to cope with Aguero - but he was barely able to have any impact before limping from the field. After stumbling under one challenge, the striker fell awkwardly while attempting to regain his balance and, following treatment, was unable to continue.
The hosts managed to recover their poise, though, and were ahead through Toure's spot-kick in the 24th minute.
James Milner - recalled to the City side along with Eliaquim Mangala and Fernando from the win at Sunderland - beat Phil Jagielka to the ball close to the byline and went down under the defender's challenge.
With Aguero off the field, Toure stepped up and placed the spot-kick into the bottom left-hand corner for his fourth league goal of the season.
Samir Nasri's powerful drive was headed away by Sylvain Distin in the 34th minute and Everton threatened for the first time five minutes later when Kevin Mirallas' first-time strike was deflected wide by Fernando.
Pozo ought to have doubled City's lead five minutes into the second half, but shot straight at the legs of Tim Howard after being picked out by Milner six yards from goal.
Milner then wasted another chance 12 minutes from time, blazing a volley over after substitutes Frank Lampard and Edin Dzeko had combined.
Hart had been relatively untroubled for much of the game, but the England international pulled off a superb one-handed save to tip Lukaku's volley around the post with eight minutes remaining.
With that stop, Everton's best chance of an equaliser came and went as City held on to secure the win and keep the pressure on Chelsea.
