Javi Gracia's team, unchanged for the sixth league game, showed why they have been the season's revelation and looked set for a fifth win in six matches only to spurn several fine chances offered largely by inept home defending.
Yet Fulham were re-energised by a tactical reshuffle after the break with Serbia striker Mitrovic becoming joint league top scorer with his fifth goal of the season in the 78th minute.
He almost got the winner with a late header that brought a brilliant point-blank save from Ben Foster and rattled the bar.
Gracia, whose side had lost their unbeaten record against Manchester United the previous weekend, told Sky Sports: "We had chances in the first half to kill the game. We didn't do it in the second and made a mistake.
"We are a little bit disappointed with just one point."
Watford were fourth in the standings on 13 points from six games, while Fulham stood in 15th place with five points before the rest of the weekend's Premier League programme.
FOCAL POINT
Mitrovic again proved the focal point of Fulham's comeback after manager Slavisa Jokanovic had made tactical changes at halftime that rejuvenated his side.
His sharp, close-range finish was his 17th league goal since his Fulham debut at the start of the year.
No player has scored more league goals across the top four tiers of the English game during that period.
The powerful Serb twice went close to sealing the points, with Foster, having tipped his header against the bar, making another fine save from Mitrovic's left-foot shot.
Watford striker Troy Deeney said he may have suffered broken bones in his foot and was going for an x-ray.
"It is what it is, probably a couple of broken bones. I'm a big ugly boy though, I'll be fine," Deeney told Sky Sports, adding he had played with three broken toes the previous week.
Deeney, an old friend of Britain's world heavyweight champion Anthony Joshua, said he was confident the injury would not stop him gong to see "AJ" fighting Russian Alexander Povetkin at Wembley later on Saturday.
(Reporting by Ian Chadband; Editing by Ken Ferris)
