Mourinho left Christian Eriksen on the bench as a first-half goal and assist from Son Heung-min helped end a run of 12 away Premier League games without a victory for Spurs, despite a late home fightback.
The Korea Republic star opened the scoring in the 36th minute and then set up Lucas Moura to get Mourinho's men up and running, Harry Kane adding to the scoreline as Spurs climbed to sixth on the table.
Michail Antonio and Angelo Ogbonna netted late consolations but West Ham continues to struggle after a bright start to the season. Manuel Pellegrini's side has now lost six of its past seven Premier League games.
Kane struck in the third minute of the Mourinho era but the striker had strayed offside from Dele Alli's pass.
Serge Aurier's clumsy aerial challenge on Robert Snodgrass in the box went unpunished before Son's snapshot tested Roberto Jimenez, the under-fire goalkeeper equal to the effort.
Roberto was beaten twice before the break, though, Alli's pass freeing Son to shuffle away from Issa Diop and lash home a powerful left-footed strike.
Son then created the second after fine work on the left touchline by Alli, the forward crossing low for Lucas to get in front of Aaron Cresswell and nudge home from close range.
Lucas dragged a great chance wide after the restart but it was soon 3-0, Aurier given too much room on the right to measure a cross Kane met with a downward header to move into third place on Spurs' all-time top goalscorers' list.
Substitute Antonio gave the home fans something to cheer about with a fine finish in the 73rd minute to deny Mourinho, who gave Eriksen a brief late cameo, a clean sheet.
After an offside Declan Rice was denied by VAR (video assistant referee), the Hammers scored a second deep into added time when Ogbonna beat Paulo Gazzaniga with a low shot from a corner, but it was too little, too late for the home side.