A Zlatan Ibrahimovic hat-trick - his first in United colours - got the job done ahead of their return fixture in France next week and Mourinho's men held a 1-0 lead at half-time thanks to a heavily deflected Zlatan free-kick.
United have already had one Premier League game, an away trip to Manchester City, postponed after they reached the final of the League Cup and their schedule could see further disruption depending on their FA Cup and Europa League progress.
Jose Mourinho's side are also chasing a top-four place in the Premier League and Ibrahimovic is keen to keep up the momentum after losing just once in 23 games.
Saint-Etienne go into the game on the back of a breezy 4-0 win over Ligue 1's bottom club Lorient, which defender Kevin Malcuit believes was helpful preparation. Everything can change but we're happy at the moment.
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Marcus Rashford made his 50th Manchester United appearance in the Europa League Round of 32 win over Saint-Etienne, nearly a year after making his debut at the same stage of the competition.
Ruffier's double save denied Juan Mata and Anthony Martial forced the visiting goalkeeper into sharp saves, while Paul Pogba headed against the crossbar from close range.
United's eventual dominance saw Ibrahimovic net his first hat-trick - a Zlat-trick even - since joining the club in summer.
In the 75th minute, substitute in the second half Marcus Rashford darted to the paint from the left, before his stitching pass found the Swede, and the latter tapped the ball into an empty goal.
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He added: "It feels good. We played an open game today and it was important to get a good result so we can take it into the second leg", Ibrahimovic said.
"We don't play Champions League, so if that is the case I would prefer to play in the Europa League than be at home watching TV". I always respect football and I know football can be nasty to you, so I go with a strong team.
The world's most expensive player, Paul Pogba, was up against his brother Florentin, who was signed by the French side for €500,000 in 2012.
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