The relief was palpable after the substitute's effort bobbled past Hugo Lloris in the 81st minute, continuing United's 100 per cent Premier League record at Old Trafford where they have not even conceded a goal.
Mourinho slammed United for a "really poor" attitude after the 2-1 defeat by Huddersfield but the Portuguese boss was far happier with what he saw against Spurs.
Speaking to Sky Sports after the game, Mourinho said: "Sometimes he starts the match and his contribution is good but he doesn't score. Today, every ball looked like the last ball of their careers".
Manchester United head into their Premier League showdown with Tottenham Hotspur at Old Trafford looking to avoid extending their winless streak in the top flight to three matches. I don't understand some reactions when people question "are they Red Devils"? "The two strikers were up against wonderful central defenders, some of the best in Europe".
United substitute Anthony Martial turned out to be the match victor, making the most of poor Spurs defending and finishing past fellow countryman Hugo Lloris.
"But I think the only team that had opportunities I think was us, apart from the Dele Alli chance, we controlled them very well".
"That was hard, it could have been a draw". Both teams were trying to win but both knew the opponent was strong.
"We tried and we deserved the victory".
The Tottenham game had an extra twinge of importance to it based on the fact that it was on the back of Mourinho's side's first sign of weakness this season.
"It was a shame to lose".
'Eric, let's see, he'll have one more training session, but he is the only one I hope from the injured group that can be ready'. "It was our mistake".