While Wolves looked to subside, Jimenez wiggled through the defence to break the deadlock with a shot on the turn after 70 minutes.
Aguero had the last laugh, however, when he headed his 28th goal of the season in all competitions, although he appeared to be offside and the Video Assistant Referee (VAR) system was not being used in the match to the dismay of the Swansea fans.
City finished the tie off with goals from Bernardo Silva and Aguero either side of a Kristoffer Nordfelt own goal - the Swansea goalkeeper unfortunate that Aguero's penalty attempt hit the post only to hit the back of him and go in.
"They ask all the clubs about the VAR and all around Europe, the VAR is there and here it's not".
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Despite the defeat, Solskjaer - whose side travel to Wolves for an FA Cup quarter-final on Saturday - has no issues with United's performance and believes they were unlucky to lose.
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City face a hectic schedule following next week's global break, including three games against Tottenham in the space of just 11 days.
However, they were opened up after 20 minutes by Connor Roberts who drew a foul from Fabian Delph in the penalty area and Matt Grimes converted from the spot to give Swansea the lead. "But the spirit and persistence helped us to win the game".
Guardiola, whose side have already won the League Cup and are through to the quarter-finals of the Champions League, added: "When you fight for all the titles you don't have rest and every three days there is a game, it is so, so healthy to win these kind of games".
In the end, Guardiola was left to sing the praises of Aguero, who had the final say in an exhilarating contest as he made up for lost time in dramatic fashion with his late victor.
Let us know in the comments. But for a long time tonight it looked like that might happen.
Police match commander Supt Steve Jones said the safety of supporters, players, officials and those who work at these games was "paramount".
United's interim manager was remarkably upbeat despite his side's flat performance.