John Terry also scored in a rare start but two defensive lapses from the 22-year Chelsea man almost allowed Watford to salvage a draw before Fabregas' late victor.
But Terry's joy was short-lived, as only 40 seconds later, the 36-year-old misplayed a defensive header in his own box that allowed Etienne Capoue to draw Watford level.
Conte thinks Terry should not retire and instead stick by his decision to continue playing regularly elsewhere, which was his motivation for departing Chelsea.
Nevertheless, Terry has now fuelled speculation he could end his career altogether once his time at Chelsea comes to an end.
"First and foremost it was great for me to get in the starting line-up", he added. "As a player that's all you want", he said.
"It was probably the hardest team I ever played against, 15 goals conceded. And the manager made that clear to me".
Chelsea wrapped up their sixth English title with a win at West Brom on Friday, and the home fans were in a celebratory mood as they welcomed the champions back to Stamford Bridge.
The Blues can break the record by beating Sunderland in Sunday's final league game.
"I knew I could get my chance against Watford, so from Saturday morning I started focusing on this game".
The Premier League trophy will be presented following Chelsea's final match of the season at home to Sunderland on Sunday.
Beaten manager Walter Mazzarri played down an on-pitch argument between Okaka and his captain Troy Deeney that occurred late in the game, but said he would speak to the pair about the matter.
'It's important to finish the season - we must try to finish in the best way possible to reach our target and to win the FA Cup, ' said Conte.
After the game, Conte was asked if he'd would be telling Costa off for taking the food.
But according to Gary Neville, Jose Mourinho has enjoyed an even better Chelsea team than the one now being overseen by Conte.