With Tottenham fairly lifeless going forward throughout, United did deserve all three points, which came as a result of Mkhitaryan's 29th minute strike following a Harry Kane mistake.
There were chances to double the lead in the second half, with Paul Pogba striking the bar, but in the end one goal was all the hosts needed.
Few clear cut chances early on
With the two teams labelled as better at the back than going forward, it was no surprise that the start to the game saw chances few and far between at either end.
The closest that either side came in the first period was a Paul Pogba effort in just the second minute. A sweeping attack from United ended with Zlatan Ibrahimovic finding his teammate, who had Hugo Lloris scrambling across his goal to save the first time strike.
Tottenham responded by looking to come forward themselves, albeit to no avail. Heung-Min Son did well to evade Phil Jones' challenge and make room for a shot, but blazed over the bar. Dele Alli was involved with Jones too, going down under his challenge as a ball came into the area, his appeals coming to nothing.
Spurs continued to put United under some pressure as they attempted to turn the screw, and it seemed as if the hosts were getting a little rattled as David de Gea screamed at his defence for not organising themselves quickly enough from a Christian Eriksen free kick, de Gea forced into a good save.
Kane error presents Mkhitaryan with opener
However, the first goal did eventually come, going the way of the home side. Harry Kane was at fault, stumbling in midfield before giving the ball away to Ander Herrera, who slipped Mkhitaryan in behind the defene, the Armenian doing the rest by sending an unstoppable shot crashing into the roof of the net.
Hugo Lloris could do nothing about the goal, but could have helped himself minutes later. Presenting defender Danny Rose with a poor pass, Lloris watched on as United pinched the ball back, and was forced into action once more as Ibrahimovic sent a low shot towards the corner from Antonio Valencia's cross. Fortunately, the Frenchman redeemed himself.
The game was creaking into life slowly, evidenced more so as Tottenham went up the other end soon after, Son cutting inside to sting de Gea's palms with a rising shot, the Spaniard tipping it over.
Pogba closest to a second
Going into the second half, Pogba came alive a little and was the closest to doubling the United lead as Spurs struggled to make any headway at the other end.
The Frenchman left Hugo Lloris rooted to the spot with a beautifully taken free-kick that pinged back off the bar, Ibrahimovic unhappy in the aftermath as he felt he'd been shoved over by Toby Alderweireld.
Pogba would have another opportunity to make it two just a minute later, playing a one-two with Mkhitaryan as the Armenian dragged the ball back to him on the edge of the box, Lloris' reactions quick as a flash to push the eventual shot wide.
Up at the other end, despite Pochettino bringing Moussa Sissoko and Harry Winks into the fold, Tottenham were still struggling for invention. Kane was doing his best despite limited support, and when he turned Rojo to win a free-kick, Eriksen again forced de Gea into a save.
Despite holding on to take all three points, there was a late blow for United as Mkhitaryan, who had enjoyed a magnificent game, was stretchered off with what looked like a twisted ankle following a coming together with Rose.