Mkhitaryan netted after 29 minutes of a contest in which United looked as confident and composed as they have since Mourinho took over as manager at Old Trafford, but the Armenian winger was taken off on a stretcher in the closing stages after injuring his ankle.
The result gave the Red Devils their first home victory in the league since September, while Spurs' winless run on the road in all competitions now stretches to eight matches.
It was the style and swagger of United's forwards that will have most pleased Mourinho, as his expensively assembled attack proved that they can win games against the league's best teams – without dominating possession.
The defeat was only Spurs' second in the league this season, but manager Mauricio Pochettino – whose side are now 10 points adrift of leaders Chelsea – will have been disappointed by his side's lack of attacking threat and a notably poor performance by Harry Kane, who was at fault for United's goal.
Mkhitaryan, who has galvanised United's attack in recent weeks, surged forward in the second minute and fed Zlatan Ibrahimovic, with his cross affording Paul Pogba the chance to draw the first save from Hugo Lloris with a low shot.
Having survived the early scare, Spurs set about enforcing their brand of possession football from deep areas of the pitch, but the steadying influence of Michael Carrick and Phil Jones at the heart of Mourinho's team made it difficult for the visitors to find openings.
Christian Eriksen stung the palms of David de Gea with a well-struck free-kick after 18 minutes, before Ander Herrera sent a long-range drive straight into the arms of Lloris and Carrick thundered an attempt over the crossbar.
United's industry paid off on the half-hour mark when Kane gave the ball away sloppily in the centre circle and Herrera released Mkhitaryan, who sprinted clear of the Spurs defence and lashed a shot high into the net, giving Lloris no chance.
Ibrahimovic should have doubled the lead moments later, but was denied by Lloris, and at the other end De Gea made a good save from Son Heung-min to keep United ahead at the break.
Eriksen was again denied by the quick reactions of De Gea in the second half, before Victor Wanyama missed a golden chance to equalise when he was presented with a free header, which he badly misdirected.
