In a drab contest in North London, an own goal from Michael Keane proved to be the difference.
The Englishman was terribly unlucky when Giovanni Lo Celso's shot rebounded off his chest and trickled past a helpless Jordan Pickford.
Tension threatened to boil over for Spurs when Hugo Lloris and Heung-min Son clashed after the half-time whistle.
Lloris pushed the South Korean in the back and the pair had to be separated by teammates before going down the tunnel.
The win keeps alive Tottenham's hopes of playing European football next season, while Everton stay in 11th.
Speaking after the game, Mourinho said: "It was not an artistic performance.
"Hugo didn't have to make great saves. Richarlison and Calvert-Lewin are a couple of the best strikers in England and we controlled them very well.
"We were speaking a lot about our attitude. The way we played against Sheffield United, someone in front who doesn't know we are fighting for a European place probably thinks we're a mid-table team.
"Today we tried to score more goals and had couple of chances with Son that could have killed the game."