South Korean forward Son Heung-min opened the scoring in the 36th minute for the visitors at London Stadium on Saturday, while Brazilian midfielder Lucas Moura doubled the Spurs' lead at the 43-minute mark on a goal set up by Son and Harry Kane made it 3-0 when he scored on a header shortly after the intermission, reports Efe news.
Michail Antonio pulled one back for Manuel Pellegrini's squad in the 73rd minute and Declan Rice appeared to cut the lead down to one early in second-half stoppage time but his goal was ruled out for offside.
Although Angelo Ogbonna later made the score 3-2 deep in injury time, there were not enough ticks left on the clock for West Ham to notch the equalizer.
Afterward, Mourinho, who did a knee slide on the sideline after Lucas's goal, said that score was particularly satisfying.
Tottenham, who with the win provisionally moved up to ninth place with 17 points, are the third team Mourinho has managed in the Premier League after Chelsea (two separate stints) and Manchester United.
The victory in this London derby was an important one for last season's Champions League runner-ups, whose winless streak in the Premier League dating back to late September had cost Mauricio Pochettino his job earlier this week.
In other Premier League action Saturday, Manchester City kept the gap between them and first-place Liverpool in single digits by defeating visiting, red-hot Chelsea 2-1.
With the win, the Citizens moved into third place past Chelsea, who had come into the match with a six-game Premier League winning streak. Manchester City now has 28 points, nine behind league-leading Liverpool.
Elsewhere, Liverpool needed a late goal from Brazilian star Roberto Firmino to secure a surprisingly hard-fought 2-1 win over Crystal Palace.
With the win, the Reds (37 points) maintained their eight-point lead over second-place Leicester City, who went on the road and defeated Brighton 2-0.
( With inputs from IANS )