Jesus hadn't scored a Premier League goal for four months before opening the scoring midway through the first-half and bulleted home a header to double City's lead early in the second-half.
Ilkay Gundogan put the result beyond doubt four minutes from time with a third goal that crowned a sublime 44-pass move.
David Silva's late goal sealed the away victory as City got their Champions League campaign back on track after the shock 2-1 defeat at home to Lyon a fortnight ago.
It has been widely reported that Guardiola has been unhappy with Sane's application in training, yet the City manager is unwilling to criticise the player in public.
Liverpool star Sadio Mane's collision with Manchester City goalkeeper Ederson was an accident and did not merit a red card, said Jurgen Klopp.
The Chilean striker struck in the 101st minute to secure an all-London May 27 final against Chelsea.