United went ahead as early as the eighth minute as Antonio Valencia cut inside and fired a fine left-footed effort into the top corner.
Stoke did not sit back and managed to carve out a couple chances, with Stephen Ireland going close on two occasions just before the 20-minute mark.
However, United doubled their lead in the 37th minute when Paul Pogba turned provider again to pick out Anthony Martial, who superbly curled into the top corner from the edge of the box.
The visitors nearly reduced the deficit just before the break but David de Ge was on hand to keep out Xherdan Shaqiri's strike, which look destined for the bottom corner.
The Red Devils had the ball in the back of the net again after 65 minutes but Juan Mata's strike was flagged offside.
The third goal eventually arrived in the 72nd minute when Romelu Lukaku shrugged off a couple challenges before drilling the ball home from close.
Substitute Mame Biram Diouf nearly bagged a consolation with four minutes remaining, but the Senegalese forward could only fire straight at De Gea from close range.
That proved to be the final chance of the half as Jose Mourinho's charges ran out comfortable winners on the night.