Jesus netted twice within 23 minutes, with Rodri drilling home a stunning third after Hassane Kamara pulled one back for the Hornets midway through an entertaining first half.
The Brazilian celebrated twice more within eight minutes of the restart as relegation-threatened Watford collapsed, Jesus first winning and converting a penalty before sweeping home from Kevin De Bruyne's pass.
All eyes will now turn to Anfield on Monday (AEST), where title challenger Liverpool will attempt to keep pace with Pep Guardiola's men by beating Merseyside rival Everton.
Jesus needed just four minutes to give City the lead, turning home Oleksandr Zinchenko's fierce left-wing cross after the Ukrainian latched onto Joao Cancelo's overhit ball.
City almost doubled its lead 10 minutes later when Ben Foster got down well to turn away Cancelo's left-footed shot, but Jesus was soon on hand to grab his second when meeting De Bruyne's excellent right-wing cross with a firm header.
Watford briefly halved the arrears when Kamara raced through to power a left-footed drive into the bottom-right corner, but Rodri restored the two-goal cushion in stunning fashion after 34 minutes, unleashing an unstoppable 25-yard volley into the top-left corner.
Jesus then completed his hat-trick just four minutes into the second half, rolling home a penalty after chasing down a poor clearance and being felled by Foster, and helped himself to a remarkable fourth four minutes later when he converted from De Bruyne's cut-back.
Riyad Mahrez could have added a sixth when sending a wild right-footed volley over late on, as City saw out an incredible 15th consecutive victory over Watford.