The Red Devils were bright and brisk in the opening half and fully meritorious of their victory overall, despite a moment of individual brilliance from Dele Alli briefly securing parity before half-time.
Rashford’s penalty early in the second half restored the advantage and gave United boss Ole Gunnar Solskjaer a timely boost as his side leapfrogged Mourinho’s in the table to climb into sixth spot.
The home side started with real purpose and got their reward early when Rashford blasted home from the angle of the 18-yard box.
Spurs dithered and the ball broke to the England forward, who wasted no time in going for goal. His shot had plenty of power but Paulo Gazzaniga will surely have been disappointed to get beaten at his near post.
Mourinho insisted he had been welcomed roundly at Old Trafford pre-game by one and all, but that wasn’t the case on 15 minutes as Daniel James slid into a challenge with Harry Winks in front of the Spurs technical area and ended up giving the Portuguese a sore knock to his shin.
On 25 minutes Gazzaniga atoned somewhat for his role in the opening goal, getting his fingertips to a fierce dipping drive from Rashford and doing enough to divert the ball onto the crossbar.
It took Spurs almost 39 minutes to mount a meaningful attack, Harry Kane and Son Heung-Min combining.
Man United failed to clear their lines and as the ball dropped towards the ground near the six-yard area, Alli pulled it away from two covering defenders before a superbly timed half-volley across David de Gea into the corner of the net.
Mourinho’s side were fortunate to go in level but their parity didn’t last long.
Rashford drove at Moussa Sissoko inside the box shortly after the restart and the midfielder upended him, with Paul Tierney quickly pointing to the spot.
Troubles they may have had early in the season with penalty kicks, but Rashford was calmness personified this time and sent Gazzaniga the wrong way.
Christian Eriksen seems set to leave Tottenham next month but the Dane was thrown in off the bench for the final 25 minutes in a bid to rescue a point.
He picked out Serge Aurier inside the box with six minutes left but the full-back’s first-time shot was straight down the bowels of de Gea.
Similarly, in stoppage time, Alli controlled inside the box and fired at goal but the Spaniard was in the right place to smother it and, with it, Mourinho’s hopes of getting anything from this Old Trafford return.