Watford almost pulled level on 26 minutes through Andre Grey but Spurs goalkeeper Hugo Lloris produced a save to keep out the striker's effort.
Tottenham have not lost in the top flight this season when opening the scoring and, though captain Hugo Lloris was required to maintain their advantage, Kane gave Watford a mountain to climb with his 48th-minute effort, moving him onto 27 league goals - four behind Liverpool's Mohamed Salah.
Kane curled in what looked to be his second just past the 70-minute mark from a Jan Vertonghen assist, but the linesman had his flag up and the England international's strike was ruled out for offside.
The Lillywhites who were without a win in their last two league games had seen the lead between them and fifth-placed Chelsea reduced to two points following the Blues' 1-0 win against Swansea on Saturday.
Lloris made a second good save to deny Richarlison, who had been played in by Will Hughes, and Spurs doubled their lead four minutes after the restart when Harry Kane sidefooted home Trippier's inviting low cross.
In the end, Spurs saw out the remaining stages with relative ease to claim three points on the night. Maybe we are not playing the way we are wanting to play but it's hard to keep playing good football'. I am very happy because the three points now put us in a very good position.
It's hard to win games. We tried but I think Watford was a very hard opponent.
Of his own form, Kane added: "I feel good". I'd like to have played better in the last few games, same as the team, but I feel good, feel sharp and could have scored more.
"I try to improve every year".