Jesus followed his five goals in two cup games last week with a first-half double as City recorded a fifth straight win in all competitions at the Etihad Stadium.
Wolves had Willy Boly sent off in between Jesus's goals, the centre-back dismissed for a lunge on Bernardo Silva although he got some of the ball, with Nuno Espirito Santo's side well beaten.
Conor Coady's late own goal completed the scoring on a particularly special occasion for David Silva, whose 267th Premier League game for City moves him above Joe Hart into top spot in the club's appearance list for the competition.
City led inside 10 minutes as Jesus continued his hot streak with his sixth goal of 2019.
Aymeric Laporte sent Leroy Sane sprinting in behind Matt Doherty and the rapid winger delivered a low left-wing cross that Jesus slid in to meet at the back post.
Wolves' task was made greater in the 19th minute when Boly, who scored with his hand when the reverse fixture was drawn 1-1, saw red for a heavy challenge on Bernardo Silva.
It was 2-0 before the break, Jesus doubling the City lead by sending Rui Patricio the wrong way from the penalty spot after Raheem Sterling was brought down by Ryan Bennett.
City had to wait for their third goal, substitute Kevin De Bruyne seeing his wicked ball into the box take a slight deflection off Wolves captain Coady with 12 minutes to go, but the message to Liverpool was clear.