The Premier League leaders had been frustrated by their Championship opponents during a goalless first half at Stamford Bridge, provoking manager Jose Mourinho into action at the interval.
Mourinho sent on Willian and top scorer Diego Costa at the start of the second half in place of Oscar and Andre Schurrle, and the two had the desired impact as both were involved in breaking the deadlock just before the hour mark.
Costa cut in from the left and passed to Loic Remy, who in turn found Willian and the Brazilian curled a sublime shot into the net from just outside the area.
With the breakthrough made, Chelsea struck a quickfire double blow in the final 20 minutes to put the result beyond doubt.
Remy volleyed in a second after Costa's shot had been blocked, and Kurt Zouma headed home a pinpoint cross from Cesar Azpilicueta.
It was a welcome victory for Chelsea, who had been stunned 5-3 by London rivals Tottenham in the league on New Year's Day, while Watford - managed by former Chelsea man Slavisa Jokanovic - will now focus their attentions on their promotion challenge.
Watford, meanwhile, showed three alterations from their 4-2 win at Cardiff City with leading scorer Troy Deeney among those to return.
Cahill diverted Schurrle's free-kick over the crossbar in the seventh minute, while the visitors' first sight of goal came when Daniel Tozser fired straight at Petr Cech from distance shortly afterwards.
The Chelsea goalkeeper was similarly comfortable in holding Deeney's drive in the 27th minute, and Cech's opposite number Jonathan Bond was tested for the first time when he had to react smartly to keep out Didier Drogba's header from Remy's delivery.
Cahill went close for a second time when he headed Filipe Luis' corner narrowly wide just before half-time.
Watford made a bright start to the second half and went close to opening the scoring in the 55th minute when Deeney's low cross took a deflection off Filipe Luis and was diverted behind by the sharp reflexes of Cech.
Remy then took advantage of a deflated Watford by thumping a 70th-minute volley high into the net, before Zouma rounded off the scoring with a powerful header two minutes later.
Watford had conceded 13 goals without reply on their previous three visits to Stamford Bridge, and in the end this meeting proved a similarly one-sided affair as Mourinho's side cruised into the fourth round.
