The Blues had to come from behind but will feel they should have claimed all three points as Oscar slipped and sent a potentially match-winning penalty ballooning into the stands with 10 minutes left.
Costa had given Chelsea a 32nd-minute lead, but Watford hit back as Troy Deeney tucked away a penalty and his ever-dangerous strike partner Odion Ighalo scored yet again after the break.
Another classy Costa finish levelled things up, but Oscar’s blooper meant a pulsating Boxing Day encounter ended with the sides sharing the spoils.
The Blues looked eager to impress early on and Costa headed Pedro’s cross just over as they monopolised possession in the first 15 minutes.
But Watford quickly found their feet and Ighalo squandered a great chance to give them the advantage, pulling his shot well wide after Jurado’s effort had fallen perfectly for him.
However, Willian’s corners were a regular source of problems for the Watford defence and Chelsea took the lead when the Brazilian’s cross bounced into the six-yard box off the heads of Gary Cahill and John Terry, and Costa swivelled expertly before volleying the ball into the back of the net.
The Blues continued to press forward nonetheless, after Troy Deeney slotted in a penalty and 11 minutes after half-time were down 2-1 thanks to a deflected shot from Odion Ighalo.
Diego Costa marred a good afternoon’s work with a booking, which means he will be banned for Monday’s big game against Manchester United.
The unlikely figure of John Obi Mikel almost sent Chelsea into that match on a high but his late shot was just wide of the target and Chelsea will go into the Old Trafford blockbuster just a couple of points clear of the drop zone.
Watford, meanwhile, emerged from another tough match with their reputation further enhanced and they sit seventh ahead of Tottenham’s visit to Vicarage Road on Monday.