Antonio Conte's side looked in control when they opened the scoring in stunning fashion through Pedro, but were pegged back when, on the stroke of half-time, Abdoulaye Doucoure equalised.
Things went sour for the champions after the break when Roberto Pereyra took advantage of some poor defending from the hosts to give Watford a 2-1 lead but substitute Batshuayi's header followed by another from Azpilicueta and then a last-gasp goal from the Belgian ensured Chelsea did not lose for the third straight Premier League game.
After seeing his Chelsea side throw away a two-goal lead against Roma in midweek and be forced to come from behind to secure a 3-3 draw, Conte dropped Andreas Christensen, who started that game in defence, in favour of summer signing Antonio Rudiger.
David Luiz, who played in a midfield position against Roma, was pushed back into defence after Conte had bemoaned how using the Brazilian further forward and changing the team's set-up meant Chelsea couldn't play their own game and control proceedings.
And Luiz - who passed a late fitness test to start against Watford - impressed back in his usual position as Chelsea took just 12 minutes to find the opener through Pedro.
The Spaniard, back in Conte's starting line-up, received Eden Hazard's ball from a corner on the right before delivering a fierce shot that smashed off the bar and into the goal.
Pedro's stunning strike injected Chelsea with confidence, but Watford fans behind Heurelho Gomes' goal were left in uproar as the corner kick from which the Chelsea winger scored should not have been given.
Conte's side proceeded in the same vein, however, and should have scored a second when a brilliant Hazard run saw the Belgian send the ball to Alvaro Morata, who then passed it cross-field to Cesc Fabregas on the right.
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The Spain international, much to Conte's disappointment, could only deliver a poor chip that Gomes comfortably claimed.
It proved a wasted opportunity as, despite Chelsea's hold on the game, they then conceded on the stroke of half-time - rather like against Roma.
This time, the goal came from the right when Luiz headed a throw-in out but saw it hit Bakayoko and fall to Doucoure. The Watford midfielder didn't hesitate when he unleashed a powerful effort that flew past Thibaut Courtois and into the goal.
The strike was undoubtedly a sucker punch for the hosts, but they still emerged from the break intent with trying to go back in front - instead going 2-1 down within minutes.
Moments after Richarlison had left Cesar Azpilicueta in his wake with a fine run forward but poked his effort just wide, the Brazilian found Pereyra in space near the back post who then drove past a hapless Chelsea defence to give Watford the lead.
Conte reacted by hauling off Morata, booked moments earlier, for Batshuayi who headed the Blues back into the game with his goal from Pedro's cross in the 71st minute.
Azpilicueta then ensured the win with his 87th-minute header before Batshuayi struck in added time to haul Chelsea to within six points of leaders Manchester City - who play later on Saturday - as Watford suffered their first away defeat in the league this season.