Son Heung-min, Lucas Moura and Harry Kane scored the goals as Mourinho made an instant impact after replacing the sacked Mauricio Pochettino on Wednesday.
Spurs were cruising at 3-0 up and although Michail Antonio and Angelo Ogbonna scored for the home side, it was too little too late.
The win rockets Spurs up the league table to sixth, but still eight points behind champions Manchester City in fourth spot, having played a game more.
"I was really happy before we conceded the two goals, we were playing well, bringing to the game things we had tried in training," Mourinho told BT Sport. "We are lucky I have so many years in the Premier League so I told the players at half-time 'even if we are 3-0 in the 85th minute the game will still be open''.