It represented a big game in which the Blues could overtake the fourth-placed Hornets, who had won three and lost one of their last Premier League fixtures.
The Blues warmed up for the game with a thrilling 3-3 draw at home to AS Roma in midweek which keeps them well on course to qualifying for the knockout stages of the Champions League.
Chelsea struck first in the 12th minute with a right-footed shot by Pedro from outside the box, assisted by Eden Hazard following a corner.
Batshuayi came off the bench to make it 2-2, with Watford having led for much of the second half through Abdoulaye Doucoure and Roberto Pereyra, before Azpilicueta and the Belgium global secured the win in the dying minutes.
The Belgian fired narrowly wide as Chelsea pushed for a victor, but it was Azpilicueta who restored the hosts' lead, heading substitute Willian's deep cross past Gomes to send Stamford Bridge - and Conte - into raptures.
"#CHEWAT just seen two glorious misses by the @WatfordFC forward".
Chelsea are still just about battling on four fronts but the clear weaknesses and holes in the squad remain following an insufficient summer transfer market.
It is safe to say that Conte's future is still going to be relentlessly questioned in the upcoming weeks. However, this win does buy him some time and it keeps Chelsea treading above water in the Premier League title race. He is fighting against history with Chelsea having had 14 managers in 16 seasons under Roman Abramovich.