The Belgium star moved onto 101 for the Blues, striking either side of Roberto Pererya's stunning volley to seal all three points for Maurizio Sarri's side at Vicarage Road.
The result puts Chelsea back in the driving seat in the race for the top four, with Arsenal having dropped points earlier in the day and champions Manchester City now only four points ahead in third place.
Willian dribbled past Ben Foster and shot wide with the best of the early chances, the incident forcing Watford to take off Christian Kabasele after he injured his arm when colliding with the post.
Hazard, again deployed as a false nine, failed to connect with Cesar Azpilicueta's cross with the goal at his mercy but made amends in first-half injury time, rounding Foster and finishing after Mateo Kovacic won back the ball in Watford's half.
However, the lead did not last until half-time, Pereyra smashing home a volley from Jose Holebas' cross to restore parity.
Watford felt they deserved a penalty when David Luiz shouldered Gerard Deulofeu to ground shortly after the break, and their frustrations were compounded 58 minutes in when Hazard scored from the spot after being brought down by Foster.
Willian and N'Golo Kante each fired narrowly wide after more fine work by Hazard, but Chelsea's one-goal lead proved enough, with Troy Deeney missing Watford's best chance for a leveller as he prodded over the bar.
19 - Eden Hazard has been directly involved in 19 goals in the Premier League this season (10 goals, nine assists); the most of any player in the competition. Leader. pic.twitter.com/Si7ZWPtv8T— OptaJoe (@OptaJoe) December 26, 2018
What does it mean? Sarri's men steal march in top-four race
It was an important result for Sarri's side given the shock defeat to Leicester City last time out, and will give them a morale lift during this hectic stage of the season.
Where would Chelsea be without Hazard?
He might not always like playing the central attacking role, but Hazard is the reason Chelsea won this game and have a two-point cushion to fifth-place Arsenal. There are few more decisive players in England.
Boxing Day blues for Foster
Chelsea failed to threaten Watford's goal too often, and when they did, they faced an out-of-sorts Foster. He went to ground too early for Hazard's first and clumsily conceded the penalty. He did at least try to make amends by going up for a late corner, which saw him attempt a bicycle-kick throughball.
Key Opta Facts
- After losing just three of their first 13 home league games under Javi Gracia (W8 D2), Watford have since lost three of their last four (W1).
- Chelsea are unbeaten in their last 14 Premier League games played on Boxing Day (W9 D5), since a 2-4 loss at Charlton in 2003-04.
- There were just 137 seconds between Chelsea opening the scoring and Watford equalising through Pereyra.