Jesus' quick-fire goals early in the second half ultimately proved enough to claim the points against the Toffees, who pulled one back through Richarlison after Claudio Bravo's mistake.
Meanwhile, Aguero, who marked his return from injury with a crisp finish in City's 2-0 win over Sheffield United, remained on the bench as an unused substitute.
Brazil international Jesus now has 13 goals to his name in all competitions this season, but Guardiola insists Aguero is still number one.
"Gabriel has been excellent, but Sergio is irreplaceable," Guardiola said. "What he means for our fans, what he's done, the goal against QPR [in 2012], we need a good back-up for all the players and Sergio has a great complimentary player in Gabriel.
"They have a great relationship."
Jesus, in a post-match interview with BT Sport, said he is still attempting to learn as much as possible from Aguero.
"Of course, it's always good to start [the year] with the victory," the 22 year-old said. "The team played well, very well. I'm happy with the goals, the guys played so well today.
"I'm a striker, I have to score and try every time. We have Sergio, who scores every game. I have to learn from him. When I go on the pitch, I have to score."
City's win kept it within a point of second-placed Leicester City, though it is still 11 adrift of runaway leader Liverpool.
Over the festive period, City beat Leicester, the Blades and Everton, though slumped to a 3-2 defeat at Wolves.
"We played great, so I am delighted for the guys. This period is so tough. We did really well. Three more points and closer to Leicester," Guardiola said. "When you are far away from the first position sometimes people give up, but we never give up.
"We have to keep going. We have FA Cup then the EFL Cup. Other teams dropped points for the top four, so it was an important win."