The Armenian found the net with less than a quarter of the match played to make sure of a comfortable route through to the last 16 of the Europa League for the Red Devils, who had done all the hard work in last week's 3-0 win at Old Trafford.
Just a second triumph on French soil for United in eight attempts, which also prolongs their run of form to one defeat in 25 overall in all competitions, was soured slightly by an injury to goalscorer Mkhitaryan and a second-half red shown to Eric Bailly.
The home side took less than two minutes to register their first attempt of the match, with Henri Saivet - one of 10 survivors from the heavy defeat at Old Trafford - testing Sergio Romero down low to send out a warning.
Saint-Etienne struggled to build any sort of pressure from that point on, though, and it was game over for the tie when Mkhitaryan found the net 17 minutes in.
That away goal meant that the French outfit, now losers in six of their last seven games against English opposition, required five goals to progress through - a feat they did not come close to achieving.
Ruffier had to be alert to stop Jordan Veretout's clearance deflecting off Vincent Pajot and into his own net, while Kevin Monnet-Paquet and Loic Perrin also had weak attempts kept out by Romero in the remainder of the opening 45 minutes.
There was to be a major blow for United prior to the interval, however, as goalscorer Mkhitaryan hobbled down the tunnel with what appeared to be a hamstring injury, just four days prior to the EFL Cup final with Southampton.
The second half panned out in the expected manner - United happy to sit back a little more and soak up the pressure, though the Ligue 1 side struggled to create any clear-cut openings.
There was to be a further blow for United after being reduced to 10 men on the hour for two needless Bailly bookings in quick succession, moments after Marouane Fellaini sent a shot into the side-netting.
Chances were few and far between for both sides, with Zlatan Ibrahimovic - the scorer of a whopping 17 goals against tonight's opponents, including all three in the reverse meeting - feeding off scraps in attack.
Bastian Schweinsteiger was given a 30-minute cameo and nearly added a second through a curled attempt, which proved to be the closest United came to adding to their tally in a flat second half.