Heuing-Min Son, Lucas Moura and Harry Kane all scored, as Spurs raced into a three-goal lead at the London Stadium.
However, the hosts fought back to score twice, through Michail Antonio and Angelo Ogbonna.
The victory also ended a run of 12 away Premier League games without a victory for Spurs.
They host Olympiacos in the Champions League on Tuesday, before Mourinho’s first home league game in charge against Bournemouth four days later.
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