Manchester United brushed the French side aside with a solid display at Old Trafford.
Zlatan Ibrahimovic was the star, scoring his first hat-trick for the club since joining on a free transfer from Paris Saint-Germain in the summer.
United travel to France for the return leg next Thursday.
Jose Mourinho has warned Manchester United against complacency
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Express Sport brings you Manchester United player ratings against Saint Etienne
And Mourinho has urged his team to focus with the EFL Cup final against Southampton coming just three days later.
"It's a good result, if you asked me before every European tie, score three goals, don't concede, I would say give me that," he told ITV Sport.
"But we know the atmosphere there, we know it's going to be still hard, we need to focus because when you go there three days later we have the final (EFL Cup).
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Zlatan Ibrahimovic scored a hat-trick as Manchester United beat Saint-Etienne
"I always fear that the players are more focused on the final than in the game, but it is important for us to make the last 16, important for us to get a result there."
United are aiming to win their second major trophy since Sir Alex Ferguson's retirement.
A win over the Saints would be their second big Wembley win in as many seasons, with the Red Devils beating Crystal Palace 2-1 to win the FA Cup under Louis van Gaal last term.