Chelsea seemed to be running out of ideas before Conte made his first change on 71 minutes, with the visitors registering just one shot on target.
But within seven minutes the Italian had rolled the dice and brought on Victor Moses, Batshuayi and Fabregas.
Batshuayi opened his Premier League account just seven minutes after coming on, reacting fastest when Heurelho Gomes spilled Eden Hazard’s shot to score.
Fabregas, an unused substitute against West Ham, then found Costa with a perfectly-weighted pass through the Watford defence – and the Spain striker did the rest.
Mazzarri loses again to his old foe
Conte and Walter Mazzarri met seven times in Serie A as managers, with the new Watford boss only coming out on top once – and that was in 2010.
The build-up was dominated by the rivalry between the two Italians and Conte admitted the pair fell out during their time coaching Napoli and Juventus respectively.
And Mazzarri seemed to have his tactics spot on for 80 minutes of the match. His side pressed well and nullified the attacking trio of Pedro, Oscar and Hazard. Wingers Jose Holebas and Nordin Amrabat also caused Chelsea’s full-backs plenty of problems.
Despite Chelsea enjoying almost two-thirds of the possession, Watford thoroughly deserved the lead when Capoue controlled Adlene Guedioura’s cross with his chest and, with acres of space in the box, rifled a left-foot shot high into the net.
But Conte sparked Chelsea into life with his changes, Watford eventually succumbing to the Blues’ relentless pressure.
Should Costa have still been on the pitch?
There were some suggestions that, for the second match running, Costa was lucky to have been still on the pitch to score the winner.
The 27-year-old had already been booked for dissent after Watford’s goal and just 10 minutes later he appeared to dive in the area but referee Jon Moss waved play on.
Against West Ham, Costa escaped a second booking when he caught Hammers keeper Adrian on the shin with a late challenge but went on to score the winner.
Match of the Day presenter Gary Lineker tweeted: “Costa scores the winner in the first 2 games. Costa lucky to stay on the pitch in the first 2 games.”
Speaking after the Watford win, Conte said: “If every game people find something on Diego it is no good for Chelsea, for Diego, it’s better to focus on the game and the match.
“For me, the first yellow is no good. I don’t accept the idea for a second yellow card for a dive but he does have to avoid the first.”
Man of the match – Michy Batshuayi
What they managers said
Chelsea manager Antonio Conte: “I’m pleased to see the reaction from my players and this win is very important for us as it gives everyone confidence. I don’t know what was wrong in the first half – but I repeat that every game in this league is tough.
“It is wrong to come to Watford and to think it’s very simple to win. In the first half I saw a good balance between the teams.
“I think we showed a great intensity in the second half and we pushed them a lot. I’m pleased for the substitutes. They didn’t start but they showed great attitude and commitment with Fabregas and Batshuayi making a real impact.
Watford manager Walter Mazzarri: “I am happy for how we played for 70-80 minutes because we played very well but I am not happy with the result.
“They scored two goals that could have been avoided. We are a team that still has room to grow and there is margin for improvement.
“The new players can help us a lot and they can help us improve as a team. We played very well so the way we played in the first half, we could have scored twice.”
Stats you need to know
Since returning to the Premier League in 2014, Cesc Fabregas has more assists than any other player (26)
Hazard collected just his second assist in 26 Premier League appearances
Capoue has scored in successive Premier League games, having scored once in 57 league games before that
Conte has lost just one of his last 32 league games as a club manager – won 29 drawn two
Chelsea have kept just one clean sheet in their past eight Premier League away games
Chelsea entertain League One side Bristol Rovers in the EFL Cup on Tuesday, with Burnley the visitors to Stamford Bridge in the league on Saturday.
Watford will look to bounce back against Gillingham in the League Cup, followed by the visit of Arsenal on Saturday.
Match ends, Watford 1, Chelsea 2.
Second Half ends, Watford 1, Chelsea 2.
Attempt blocked. Victor Moses (Chelsea) left footed shot from outside the box is blocked. Assisted by Eden Hazard.
Valon Behrami (Watford) is shown the yellow card for a bad foul.
N’Golo Kanté (Chelsea) wins a free kick on the right wing.
Foul by Valon Behrami (Watford).
Michy Batshuayi (Chelsea) hits the bar with a left footed shot from the centre of the box. Assisted by Victor Moses.
Gary Cahill (Chelsea) wins a free kick in the defensive half.
Foul by Odion Ighalo (Watford).
Eden Hazard (Chelsea) is shown the yellow card.
Foul by Eden Hazard (Chelsea).
Abdoulaye Doucouré (Watford) wins a free kick in the attacking half.
Attempt blocked. Michy Batshuayi (Chelsea) right footed shot from the right side of the box is blocked. Assisted by Eden Hazard.
Substitution, Watford. Juan Zuñiga replaces José Holebas.
Attempt missed. N’Golo Kanté (Chelsea) right footed shot from outside the box is too high. Assisted by Victor Moses.
Substitution, Watford. Matej Vydra replaces Adlène Guédioura.
Goal! Watford 1, Chelsea 2. Diego Costa (Chelsea) right footed shot from the left side of the box to the centre of the goal. Assisted by Cesc Fàbregas with a through ball following a fast break.
Offside, Watford. Nordin Amrabat tries a through ball, but Adlène Guédioura is caught offside.
Delay over. They are ready to continue.
Substitution, Watford. Abdoulaye Doucouré replaces Etienne Capoue because of an injury.
Delay in match Etienne Capoue (Watford) because of an injury.
Goal! Watford 1, Chelsea 1. Michy Batshuayi (Chelsea) right footed shot from the centre of the box to the bottom right corner.
Attempt saved. Eden Hazard (Chelsea) right footed shot from outside the box is saved in the centre of the goal. Assisted by Cesc Fàbregas.
Offside, Chelsea. John Terry tries a through ball, but Branislav Ivanovic is caught offside.