Also, Tottenham Hotspur moved back into fifth, leapfrogging London rivals Arsenal with a 2-0 victory at bottom club Swansea City.
Manchester City marched on as in-form Raheem Sterling set up their win with a goal after 38 seconds.
Swansea’s plight under new manager Carlos Carvalhal looked as precarious as the one now also facing West Bromwich Albion’s Alan Pardew.
Andy Carroll scored twice in West Ham United’s 2-1 comeback win over the Baggies.
Crystal Palace’s revival under Roy Hodgson continued apace as they also came from behind to win 2-1 at Southampton and pull clear of the relegation zone.
Manchester City’s relentless charge after a record 18 straight league triumphs may have been checked in the goalless draw at Palace on Sunday but normal service seems to have been resumed.
The unbeaten league leaders did so with dramatic swiftness.
Sterling scored his ninth goal in nine home league matches after Watford’s defence were caught napping in the opening seconds.
Then, Christian Kabasele sliced an attempted clearance into his own net in the 13th minute.
Sergio Aguero sealed the victory in the 63rd minute before a late Watford consolation from Andre Gray.
The win put City on 62 points from 22 games, 15 clear of their cross-city rivals Manchester United.
However, champions Chelsea have the chance to go second, albeit still 14 points behind, if they win at Arsenal on Wednesday.
At the other end, Swansea and West Brom can now see an alarming gap opening above them as they both sit on 16 points, four behind 18th-placed Stoke City.
Southampton are 17th, also on 20 points alongside Stoke, while West Ham moved out of the danger zone to 16th on 21.
Palace, rock bottom for so long at the start of the campaign, move up to 14th on 22.