Going into the game United had failed to win its last three games in all competitions, while Spurs had won their last three since Mourinho replaced Maurizio Pochettino.
United took the lead in the sixth minute through Rashford who in from a tight angle.
Spurs were back on level terms as Alli produced a brilliant bit of skill, raising the ball over his marker inside the box before slotting it past David De Gea.
In the 49th minute, United went 2-1 up as Rashford struck again this time from the penalty spot after he was fouled by Moussa Sissoko.
The win moves United to sixth on 21 points in the league table while Spurs are eight on 20 points.
At Stamford Bridge, Chelsea ended their winless run with a hard-fought 2-1 win against Aston Villa.
Tammy Abraham and Mason scored in either half to halt Chelsea’s run of three consecutive games without a win in all competitions.
Villa’s goal was scored by Trezeguet late in the first half.
Abraham broke the deadlock in the 23rd minute after heading in a cross but Trezeguet equalized for Villa on 41 minutes as he bundled in a cross into the back of the net.
But three minutes into the second half, Mount scored what proved to be the winner following a well-taken strike.
And at the King Power Stadium, Leicester continued their impressive run of form as they beat struggling Watford 2-0.
The win saw Leicester return to second on the log on 35 points with Watford rooted to the bottom of the standing.
Vardy put Leicester 1-0 ahead on 55 minutes from the penalty spot before Maddison sealed the win in the 90th minute.
In other games played Southampton climbed out of the relegation zone thanks to their 2-1 home win against Norwich City and Wolverhampton Wanderers beat West Ham 2-1.
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