Ken Sema put the Hornets ahead early on at Vicarage Road when he slotted home after Joao Pedro's low effort was turned into his path.
Watford captain Nathaniel Chalobah headed in 10 minutes into the second-half before Andre Gray wrapped up the points in the closing stages.
The victory moved second placed Watford six points clear of third placed Swansea City.
Swansea missed a chance to close the gap as it crashed to a 1-0 defeat in the south Wales derby against Cardiff City at Liberty Stadium.
Aden Flint's eighth-minute header kept Cardiff in the hunt for a play-off berth, with the Bluebirds four points adrift of the top six.
Cardiff's victory avenged its loss at home to Swansea earlier this season, ensuring neither team has ever done the league double over their bitter rival in the long history of the fixture.
After slipping up against Forest, fourth-placed Brentford is seven points behind Watford in the race for automatic promotion via a top-two finish.
Ivan Toney's penalty, his 28th league goal of the campaign, put Thomas Frank's side ahead in west London, but Filip Krovinovic equalised for Forest.
Like Watford, Norwich City was relegated from the Premier League last season and is firmly on course to climb back into the top-flight.
The Championship leader was held to a 1-1 draw by Blackburn Rovers at Carrow Road but still have an eight-point lead over Watford.
Daniel Farke's men looked on course to make it 10 successive league wins when Kenny McLean put them in front with a crisp finish after an exchange of passes with Kieran Dowell.
But Blackburn's Sam Gallagher headed in to stall the Canaries' promotion push.
At the other end of the table there were crucial wins for both Rotherham United and Sheffield Wednesday in their battle against the drop.
Jordan Rhodes scored twice as second-bottom Wednesday won 2-1 at Yorkshire rival Barnsley, who pulled one back through Carlton Morris.
Third-bottom Rotherham was a 2-0 winner at Bristol City as Michael Smith and Richard Wood got on the scoresheet.
Wednesday is six points from safety with a game in hand, with Rotherham three points behind fourth-bottom Birmingham. City
Bottom club Wycombe Wanderers drew 0-0 at Coventry City, while Wayne Rooney's Derby County lost 1-0 at Stoke City.
Yakou Meite scored his third goal in three games as Reading came from behind to draw 1-1 at home to Queens Park Rangers, who led at half-time through Lyndon Dykes.
Millwall beat Middlesbrough 1-0 at The Den thanks to Grant Hall's own goal, while Luton Town defeated Preston North End 1-0 with an own goal from Daniel Iversen.