The ex-Sweden international scored twice in the final 15 minutes at Old Trafford to well and truly swing the tie in the Red Devils' favour, following what had been a well-contested match up until that point.
A first treble in the colours of United for Ibrahimovic, who now has a whopping 17 career goals against Saint-Etienne, also extends their unbeaten home record in European competition to 15 without defeat and sees them take a giant step towards the last 16.
United's unchanged backline failed to settle in the opening stages, with Eric Bailly twice at fault for letting the visitors - who were previously unbeaten in 10 European games - in behind.
The fortunate breakthrough goal arrived 15 minutes in after Zlatan Ibrahimovic got to the ball ahead of Jordan Veretout to win his side a free kick 20 yards from goal, which he sent past Ruffier at a snail's pace via a deflection off the wall.
Saint-Etienne edged the remainder of the first half, seeing a penalty shout turned down when Daley Blind caught Jorginho with a trailing leg, while Henri Saivet blasted two attempts narrowly wide of the target.
Hamouma also saw his goal-bound shot blocked aside by Bailly as the opening 45 minutes transpired, moments before Monnet-Paquet's shot deflected off Chris Smalling and ended in the welcoming hands of stand-in keeper Sergio Romero - one of two changes from last time out, along with the addition of Marouane Fellaini in midfield.
United themselves had a couple of decent openings to extend their advantage, though, as Juan Mata and Martial both forced saves out of Ruffier in a lively encounter.
The second period began in a stop-start manner due to a succession of collisions, including a Martial elbow on Kevin Malcuit which did not look intentional.
Ruffier was by far the busier of the two keepers, denying Martial at the end of his latest mazy run after seeing Ibrahimovic's header ruled out for offside.
A pivotal moment in the tie arrived 15 minutes from the end of the first leg, with Nolan Roux coming off the bench and lifting a shot over Romero but only on to the roof of the net, but Ibrahimovic made no mistake at the other end by converting from a similar range after Marcus Rashford's cutback was helped into his path.
Jesse Lingard blasted a shot wide as the final stages closed in, though the decisive moment did arrive 88 minutes into to match when Ibrahimovic was sent to the ground inside the box, before brushing himself down to complete his treble from the spot.