The temperamental Costa, so often the London club's villain during a campaign where he has frequently looked completely off the pace, netted in the 32nd and 65th minutes to take his season's goal tally to five in the Premier League.
The Spain striker, however, blamed by some fans for the sacking of Jose Mourinho earlier this month and booed off the pitch against Sunderland last week, was cautioned for a rash late challenge and will miss champions Chelsea's trip to Old Trafford.
"He's out which means we have to solve that problem in 48 hours," new interim coach Guus Hiddink told reporters at Stamford Bridge. "It's a pity as he was going well after a good performance.
"He focussed himself where he's good and when he does that he's very dangerous. (I told him) not to waste extra energy where he doesn't need to."
Mourinho, dismissed because of Chelsea's precarious position near the relegation zone, has been linked by media reports with a move to United where coach Louis van Gaal is under fire following a string of poor results.
The Chelsea crowd, vocal in support of Mourinho last week, were muted on Saturday.
There were few banners lauding the Portuguese, the chants for him dried up and Mourinho masks appeared in the stands at the Britannia Stadium rather than Stamford Bridge as United lost 2-0 to Stoke City on Monday.
Chelsea, who are sixth from bottom. were reined in by an industrious Watford side who are seventh in the table.
A 42nd-minute penalty by captain Troy Deeney after Nemanja Matic handled and a deflected 56th-minute shot from Odion Ighalo gave the promoted team hope of claiming another top scalp.
Chelsea heads may have dropped earlier in the season but they kept forcing Watford back and should have gone 3-2 up 10 minutes from time when Brazilian Oscar slipped and sent a penalty high over the bar.
"He shouldn't have worn slicks, he should have put on normal tyres," joked Hiddink before adding he was happy with the way his players had fought back from 2-1 down.
"The team had to react and the team did. They showed ambition, if they show ambition the crowd reacts positively."
(Editing by Tony Jimenez)
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