The defending Premier League champions beat Sunderland 3-1 last weekend in their first game following the departure of Jose Mourinho - Hiddink had a watching brief from the stands as Steve Holland and Eddie Newton took charge of the first team - and looked set to be maintain that momentum when Diego Costa put them ahead.
However, Quique Sanchez Flores' side were unperturbed and drew level before the break when Troy Deeney converted a cool penalty following a needless handball from Nemanja Matic.
Watford continued to look dangerous after the interval and moved ahead in the 56th minute, Odion Ighalo setting a new club record by scoring in the fifth successive Premier League match.
The visitors were denied a historic away win when Costa equalised before Oscar passed up the chance to secure all three points and successive Premier League wins for the first time this season for Chelsea when he sent his spot-kick over with 10 minutes remaining. Chelsea were handed a further blow when Costa was shown a yellow card for late tackle on Craig Cathcart in the closing stages, ruling him out of their next match against Manchester United.
Hiddink made one change to the Chelsea team for his first game back at the helm, replacing Kurt Zouma with Gary Cahill, while Sanchez Flores' only switch was enforced as Jose Holebas came in for Nathan Ake – ineligible against his parent club.
The hosts started with a high tempo and had a pair of chances inside 10 minutes, but Costa sent his header over and Willian saw his deflected free-kick deflect off Almen Abdi loop narrowly wide.
Hiddink's side struggled to create clear openings, though, and Watford started to grow in confidence and become more adventurous.
Ighalo was unable to convert either of the two chances that came his way inside the opening half-hour and Watford were made to pay as they fell behind with 32 minutes played.
John Terry's header deflected off Cahill and fell kindly for Costa, who lashed a clinical volley into the top corner.
Oscar blazed a chance to double Chelsea's advantage over from Branislav Ivanovic's cutback soon after, and Watford were handed a lifeline in the 42nd minute.
Matic was found guilty of an inexcusable handball inside the box and Deeney took full advantage, sending Thibaut Courtois the wrong way from the spot to level the score.
In a bid to disrupt the link-up of Deeney and Ighalo, Hiddink replaced Cesc Fabregas with John Obi Mikel for the second half.
Courtois was forced down to his left to keep Etienne Capoue's 20-yard shot out the bottom corner in the 56th minute, but Watford had their second one minute later.
Ighalo was not closed down as he dribbled into the box and his left-footed strike deflected off Cahill, wrong-footing Courtois and sneaking inside the near post.
Ben Watson put in a sublime block to deny Pedro just after the hour-mark, but Costa restored parity when he latched onto Willian's throughball and guided a shot beyond Heurelho Gomes.
Eden Hazard, making his return from a hip injury as a substitute, won his side a penalty with 10 minutes remaining, but Oscar lost his footing and fired over from the spot.
Key Opta stats:
- Chelsea are unbeaten in the Premier League on Boxing Day since 2003, winning six and drawing five matches since then.
- Watford have won just two of their last 14 league matches played on Boxing Day (W2 D5 L7).
- The Hornets have already won more points in 2015/16 than in any of their previous two Premier League campaign (29).
- Diego Costa scored his first Premier League brace since January 17th versus Swansea City and it was only the second time that he has scored more than once in a single PL game at Stamford Bridge.
- Watford have won just two of their last 14 league matches played on Boxing Day (W2 D5 L7).
- The Hornets have already won more points in 2015/16 than in any of their previous two Premier League campaign (29).
- Diego Costa scored his first Premier League brace since January 17th versus Swansea City and it was only the second time that he has scored more than once in a single PL game at Stamford Bridge.