The build-up to yesterday's contest was dogged by talk of Aguero's supposed discontent at the Etihad Stadium as Guardiola continues to rotate his starting XI.
Aguero, City's all-time leading scorer, is reported to have held talks with club owner Khaldoon Al Mubarak, but he showed no signs of unhappiness against Bournemouth as he scored twice and set up a goal for Raheem Sterling.
"I respect Sergio a lot, about all he has done and what he will do in the future," said City manager Guardiola after the Premier League leaders' 17th successive league win.
"Aguero is a special player, a legend, and I am so happy when he plays good and he is scoring goals. I know the players who normally don't play are upset, but all the team deserve to play."
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Aguero's first goal, a clinically taken diving header after 27 minutes following a fine Fernandinho cross, was his 100th City goal at the Etihad.
Sterling doubled City's lead in the 53rd minute, thrashing a low effort home to end a challenging week that saw him racially abused at the club's training ground last weekend by a man who was jailed for 16 weeks on Wednesday.
- Sterling 'is loved' -
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"With and without the ball he's so aggressive and so intense. I like how clear it's becoming -- he knows when to dribble and when to pass," said the former Barcelona and Bayern Munich coach.
"Before there was a mistake, now he's enjoying scoring goals. In the past it was a bit scary for him.
"He's loved in the locker room, he's a young player and important for the national team. He must maintain that level."
Aguero nodded home his second header of the match before substitute Danilo ruthlessly finished from 12 yards out with five minutes remaining.
Although they slipped into the relegation zone, Bournemouth showed enough intent and commitment to suggest they can avoid the drop.
"City are an outstanding team, very difficult to play against and we came with a game plan to stay in the game then maybe have a go," said beaten manager Eddie Howe.
"For long periods we were good. The (first) goal came from our mistake, which was disappointing, but the rest of the half was OK. The second goal was the killer. We had another go, but it was difficult."
"If you get it wrong here they have the players to expose it. We've had an incredibly difficult run, but we are through it and have to focus on the games coming up.