David Silva and Nolito were also on target as City, with Joe Hart again on the bench, eased to victory in the first leg of their play-off in Romania and maintained Pep Guardiola’s winning start.
City’s success would have been even more convincing had Aguero not missed twice from the spot in the opening 20 minutes, continuing a poor European record, but ultimately that will probably not matter.
The tie looks beyond well Steaua heading into next week’s second leg in Manchester.
Whether or not the Romanians will face a City side containing Hart remains to be seen. Guardiola again left the England number one on the bench and rumours that his future may lie away from the Etihad Stadium are growing.
Yaya Toure was also left watching at home in Manchester after being omitted for a second successive game and some pertinent questions over City’s future make-up still need to be clarified.
None of this was evident on the pitch, however, as City flew out of the blocks in impressive fashion.
And, just as against Sunderland at the weekend, the revitalised Raheem Sterling won a penalty at Arena Nationala in the opening minutes.
Muniru Sulley was the guilty party but Aguero could not take advantage from the spot as Florin Nita saved and Nolito fired the rebound against the crossbar.
Aguero went close to making amends with a shot that flew over but Silva made no mistake as he rifled home a shot on 13 minutes after Sterling robbed Alin Tosca.
Aguero should have increased the lead after 20 minutes but again failed from 12 yards, this time after Aleksandar Kolarov was impeded, by blasting over. Remarkably, it was his fourth penalty miss from his last five in European competition.
But despite this shortcoming, City looked irresistible at times with Sterling, Silva and Kevin De Bruyne buzzing menacingly.
Kolarov twice went close as he had a shot deflected narrowly over and then volleyed against the bar from a corner. Sterling might have done better when he got behind the defence but Nita did well to tip over.
Aguero finally got on the scoresheet four minutes before the interval, clinically firing home from 18 yards after racing onto a Sterling cross.
City did have a few moments of alarm with Steaua captain Nicolae Stanciu teeing up Jugurtha Hamroun and having an effort himself, but Willy Caballero — under obvious pressure to perform as Hart’s replacement — dealt with both.
City made the result safe four minutes into the second half after another prolonged spell of possession which began when Fernandinho brought the ball from deep.
It ended with De Bruyne picking out Nolito with a clever pass into the six-yard box and the Spaniard rounding the keeper for his first City goal as Steaua appealed for offside.
With the job done, City went quiet for a spell but hit their stride again in the latter stages with Sterling testing Nita and Silva firing over.
Aguero then claimed the fourth with a crisp shot after combining well with Nolito and completed his treble in the 89th minute after racing through and clipping in a shot off the post.
Nita, Enache, Tamas, Tosca, Momcilovic, Achim (Bourceanu 46), Sulley (Ovidiu Popescu 66), Popa, Stanciu, Hamroun, Golubovic (Tudorie 46).
Cojocaru, Mitrea, Aganovic, Daniel Popescu.
Caballero, Zabaleta (Sagna 69), Otamendi, Stones, Kolarov (Clichy 75), De Bruyne (Fernando 80), Fernandinho, Silva, Sterling, Aguero, Nolito.
Hart, Navas, Delph, Iheanacho.
Daniele Orsato (Italy).
- UEFA Champions League Play-Off First Leg: Ajax 1 Rostov 1; Dinamo Zagreb 1 FC Red Bull Salzburg 1; FC Copenhagen 1 Apoel Nicosia 0; Young Boys 1 Borussia M’gladbach 3.