For large spells his side produced a vastly improved performance from the one that saw them beaten on penalties by Queen of the South five days earlier.
However with the scores tied at the interval there was an air of nervousness that only lifted when Lee McCulloch’s strike added to Dean Shiels’ opener and Lewis Macleod’s first for the club to make it 3-1 on the hour mark.
Anestis Argyriou's own goal equaliser had the 45,081 crowd on edge but a more clinical second half display, rounded off by Robbie Crawford also grabbing his first for the club, left McCoist a happy man.
The visitors might have provided a shock early in the game had the enjoyed a little more fortune.
After cracking the post from a corner in the second minute it took a smart stop from Alexander to smother a chance just a minute later.
The home side seemed to heed the warning and upped their level, enjoying the bulk of the possession.
Dean Shiels had a half chance in the opening ten minutes and should have had another attempt on the 20 minute mark.
Fine work from Lee Wallace on the left hand side saw him roll it in to the path of the Northern Ireland international.
Rather than shoot however, he laid the ball in to the path of McCulloch who screwed his effort wide of the post from the edge of the area.
However the two would combine to far greater effect to earn the breakthrough for McCoist’s side midway through the half.
The skipper won a towering header to flick the ball in to the path of his strike partner and this time Shiels didn’t pass up the opportunity.
He took a couple of touches to set himself and drove the ball low beyond David Crawford in the visitors’ goal.
The lead was short lived however with a sloppy equaliser conceded within six minutes.
Rangers may have complaints about the award of the free kick that led to the goal, but McCoist won’t be overly impressed by how his side defended the set piece.
A wicked delivery from Ricky McIntosh swung towards Alexander’s goal and Gary Wood claimed the merest of touches but it looked like Argyriou was responsible for the levelling goal.
A late corner after good work from Wallace on the left almost earned the lead again as Emilson met the set piece, but glanced his header just wide of the post.
McCoist needed more from his team in the second half and he got it in the 15 minutes immediately after the interval.
Barrie McKay almost restored the lead but dragged his shot wide from eight yards with just five minutes of the half played.
It would be another youngster who would make the difference five minutes later when Macleod showed delightful ability to turn in the box and drill low in to the corner for his first senior goal.
The 55th minute also saw another first with the introduction of the latest midfield product of Auchenhowie, Fraser Aird.
The Canadian born Scot had enjoyed the experience of being on the bench in midweek and almost had an immediate impact when he replaced McKay.
His early cross from the left almost found Anestis Argyriou at the back post, but the Greek didn’t commit himself to the delivery, to the frustration of McCoist on the touchline.
The manager’s disappointment would be tempered within minutes however as he saw his side earn a two goal cushion through his captain.
Macleod was again at the heart of the move and would have earned a free kick as he was tripped on the edge of the area, had the ball not broken in to McCulloch’s path.
A simple stab at it was enough to beat Crawford and signal a more comfortable looking final half hour than had been anticipated at the break.
The cushion allowed the introduction of yet another young midfield talent with Crawford replacing Shiels, and he too would notch his first for the club.
It was a brilliantly controlled finish from the 19-year-old, who recently signed a new five year deal at the club, tucking it home from the 12 yards, using the pace in the cross.
RANGERS: Alexander; Faure, Perry, Emilson, Wallace; Argyriou, Macleod, Black (Sandaza), McKay (Aird 55); Shiels (Crawford), McCulloch.
SUBS: Gallacher, Stella.
GOALS: Shiels (27), Macleod (55), McCulloch (60), Crawford (82).
MONTROSE: David Crawford, McNalley, Lunan, Campbell, Ricky McIntosh (McGuire 69), Gray (Winter 78), Jonathan Crawford, Masson, Young, Leighton McIntosh (Johnston 69), Gary Wood.
SUBS: Sandy Wood, McLeish.
BOOKED: Masson, Lunan, J.Crawford
GOALS: Argyriou 35 og
REFEREE: Stephen Finnie