The 20-time English champions were looked to exact revenge for their 2-0 loss to Spurs in the Premier League at Wembley back in February.
England international Dele Alli broke the deadlock in the 11th minute before Alexis Sanchez levelled midway through the first half.
Ander Herrera netted a 62nd-minute winner at Wembley to secure a place in the FA Cup final against Chelsea FC.
Manchester United are in second place in the Premier League table but a long way behind leaders Manchester City.
The Red Devils lost 2-1 to La Liga giants Sevilla in the Champions League round of 16.
Speaking at his post-match media conference about Manchester United’s character in the FA Cup semi-final, Mourinho said:
“I think that you don’t get strong with happiness in negative moments, with ‘let it go because we just lost a football match’.
“I think you grew up with criticism, with pressure and intense work – not just tactically but also mentally.
“I think the boys are growing up and it was two very good performances this week, using almost every player of the squad in these two matches and I think everybody as a group is very happy to go back to Manchester with a place in the final.”
Manchester United signed Sanchez in a swap deal from Arsenal in the January transfer window.
The Red Devils finished in sixth place in the Premier League last term but Manchester United won the Europa League and the League Cup in Mourinho’s first season in charge.
The 20-time English champions haven’t won the Premier League title since 2013.
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