Aguero became the top non-European goalscorer in Premier League history when he opened the scoring in the 24th minute, before Liverpool forward Sadio Mane was sent off for a rash aerial lunge on Ederson that saw the City goalkeeper leave the field on a stretcher.
Guardiola's side were merciless in making the numerical advantage count and Jesus headed home Kevin De Bruyne's cross in first-half stoppage time before Aguero teed him up for a simple finish when through one-on-one with Reds keeper Simon Mignolet early in the second period.
Debate over whether Brazil international Jesus or Argentina star Aguero should lead the line for City has been rife since the former's arrival from Palmeiras in January, given Guardiola's general preference for operating with one central striker.
"I don't say to the striker pass the ball, I say score a goal please," Guardiola told reporters.
"[But] it means a lot to me, what Sergio did. A lot. They are both good guys. Both are exceptional players, their relationship is top.
"Of course, both want to score goals and we need that, that egoism, wanting to score more than your team-mate, but they have the ability to choose the right decision like Sergio did.
"He was one-against-one with the goalkeeper but had the ability to pass the ball. When this happens the next time, Gabriel is going to do it for Sergio, and that's good."
Substitute Leroy Sane completed the scoring with a brace, while De Bruyne played an instrumental role in most of City's good work.
The Belgium international hopes Saturday's victory can act as a turning point for City, who only won two out of 10 league games against top-six rivals last season to significantly undermine their title bid.
"My man..." pic.twitter.com/QrynRVxcym— Manchester City (@ManCity) September 9, 2017
"The only thing we didn't do last year was win the big games," De Bruyne told reporters. "I thought we deserved to win a few more games than we did, especially at home, like the ones against Tottenham and Chelsea.
"It makes a difference – that's five or six points extra and they are losing those points so then you are closer together.
"Everyone wants to win, especially when you have a couple of years when you don't win a lot.
"Maybe there's more of an urgency to win something between the players, and I have a good feeling about this season, but you never know.
"The guys who have come in are very good additions, and I think they really suit the style we play."