Aguero, a £38 million signing from Atletico Madrid, made it 2-0 from close range in the 68th minute after Edin Dzeko had broken the deadlock 11 minutes earlier.
Man of the match David Silva added the third before Aguero capped a delightful performance with a spectacular 30-yard finish in stoppage time.
City manager Roberto Mancini – who was delighted with the team’s performance – said that Aguero’s performance was all the more astonishing as he wasn’t 100percent back to his best.
“I think he needs to recover as he only finished the Copa America three weeks ago,” saiod Mancini.
“He needs another two to three weeks to be 100 percent, maybe. For me he’s a fantastic striker, young, and he’s going to be a fantastic player for us.”
Aguero also got the thumbs-up from club captain Vincent Kompany.
“He’s come in with a surprise. The great thing for me was that he was defending too. That’s important,” said the Belgian.
Swansea manager Brendan Rodgers said that he wasn’t too depressed as his side wouldn’t play the equivalent of City every week.
“I said to the players I was proud of them,” he said.
“Up until the hour I thought we were fantastic.
“I was disappointed with two quick goals, but we conceded goals against a terrific team.”
Swansea are back in England’s top-tier for the first time since 1983. And a visit to City represented a daunting start for them even though the hosts were without Carlos Tevez, who was not considered fit enough to start.
Considerable investment has once again been ploughed into Mancini’s squad, with £50 million spent and counting.
In contrast, Swansea have conducted a moderate recruitment drive compared to City with striker Danny Graham, the £3.5 million signing from Watford, the most expensive arrival.
Graham was included in the starting line up along with Michel Vorm, the keeper signed from Utrecht, and Steven Caulker, who has joined on loan from Tottenham.
And both had their work cut out as frustrated City did everything but score during a goalless first half.
The visitors had dominated the opening exchanges when Micah Richards narrowly failed to get on the end of Silva’s 16th minute cross.
Silva is proof that there is still plenty of exceptional Spanish talent left in the Premier League despite Cesc Fabregas’ departure to Barcelona.
City’s World Cup winner let fly with a vicious 23rd minute effort which was heading for the top corner before Vorm made a spectacular one handed stop.
The Welsh team’s bar was rattled on the stroke of half-time by Gareth Barry in what had become a one-sided contest.
But City made their dominance count after half-time with four goals in the space of 33 minutes.
Dzeko was in the right place at the right time to break the deadlock from close range after Adam Johnson’s curling 57th minute effort was parried into the striker’s path by Vorm.
Aguero received a rousing reception when he replaced Nigel De Jong in the 59th minute and nine minutes later the striker was celebrating his first goal in a City shirt after connecting with Richards’ low cross.
Silva made it 3-0 in the 71st minute after Aguero turned provider before the debutant capped a fine display with a stunning 30-yard finish.
