David Silva and Nolito were also on target against the crestfallen former European champions who were spared an even heavier defeat as the visitors hit the woodwork three times.
Borussia Moenchengladbach also took a big step towards qualifying for the group stage with a 3-1 victory at Swiss side Young Boys.
Former European champions Ajax Amsterdam were held 1-1 at home by Russians Rostov while Croatian champions Dinamo Zagreb also had to settle for a 1-1 draw at home to Austrians Salzburg.
Copenhagen beat APOEL Nicosia 1-0 in the evening's other match.
City's visit to Romania got off to an extraordinary start as Aguero fluffed his lines.
The Argentine, who has missed four of his last five penalties in European competition, saw his first spot kick saved by Florin Nita after eight minutes and then shaved the crossbar with another attempt 12 minutes later.
Even so City found little resistance and took the lead in between when Silva fired home after neat footwork by Raheem Sterling.
Aguero finally found the target four minutes before halftime when he sidefooted the ball in from 18 metres following another chance created by Sterling.
Nolito and Aleksandar Kolarov also hit the woodwork in the first half for rampant City.
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