The Armenian scored his first Premier League goal as United closed the gap on Mauricio Pochettino’s men, although he was stretchered off with an ankle injury late on.
Henrikh Mkhitaryan’s bitter-sweet day marked Manchester United’s first Premier League win at Old Trafford since late September.
Mkhitaryan – making only his third league start – crashed in the first half winner but was taken off on stretcher after collapsing under a foul from Danny Rose.
It will be a grave concern for Mourinho, who froze Mkhitaryan out of the first team for almost two months but has seen the Armenian become a firm fans’ favourite.
The narrow victory – after four successive home league draws – takes United to within three points of fifth-placed Spurs, who enjoyed large spells of second half pressure but never really looked like claiming a share of the spoils.