The sides, both fresh from Scottish Cup victories in midweek, served up a hard-working 90 minutes in which effort was plentiful but clear-cut opportunities were something of a scarce commodity.
Rovers were probably worthy of their win, having created more going forward, although Gus McPherson’s side were in no way outclassed and had a few close chances of their own.
But a shrewd second-half substitution by Rovers boss John McGlynn and a goal from a set piece would be the factors separating the sides at the end of the afternoon.
Both teams tried to make good use of the ball when they had it and the Ton signalled intent as early as the fourth minute, as Gary Oliver swung a cross from the left into a busy box and Darren Hynes fired narrowly wide on the half-volley.
Reghan Tumilty was on the ground when he managed to get in an angular low shot during a Raith attack on 14 minutes but it did nothing to trouble Greenock ‘keeper Aidan McAdams.
The first of six yellow cards – three for each side – was shown after 21 minutes by referee John Beaton when Raith’s Adam King made a heavy challenge on Lewis Strapp, who was himself cautioned in the second half.
Rovers had been trying to probe for weaknesses with Dylan Tait, Kieran MacDonald, Gozie Ugwu, Reghan Tumilty and Manny Duku pusing forward in different combinations at various times.
A chance looked to have come in the 23rd minute as Ugwu rose to meet MacDonald’s cross from the left, after fine work on the opposite flank by Duku and Tumilty, but his header was yards over the bar.
At the opposite end, Stephen McGinn almost punished an error on 32 minutes with a right-foot shot from the edge of the box which went uncomfortably close.
McGinn also picked up a slack ball given away by King shortly before half time but the move, involving Reece Lyon and Sean McGinty, eventually disintegrated.
Six minutes into the second period, Hendry shot narrowly past McAdams’ right-hand post after a quick one-two with King .
This was followed on 58 minutes by probably Raith’s best chance thus far, as Armstrong crossed for what looked like a great opportunity for Duku but he headed over the bar.
The Rovers striker had been booked a few minutes earlier, while referee Beaton also cautioned his team mate Armstrong, plus Ton’s ‘keeper McAdams and Luca Colville.
Rovers reshuffled the pack on 64 minutes, with Armstrong being replaced by Jamie Gullan and Lewis Vaughan coming on for Ugwu.
The home side had looked marginally the more threatening for some time and it looked as if a goal may arrive eventually, although it was by no means a foregone conclusion. Another good Raith effort went wide of the goal, while Vaughan headed over from inside the box.
Then, with 10 minutes remaining, the deadlock was broken. A corner from Hendry was headed very near the target by Duku but Gullan made sure by striking the ball home forcefully from close range. Morton’s defence claimed a hand had been used but their appeals were to no avail.
Frankie Musonda was named Raith supporters’ man of the match over the PA system but seconds later almost suffered some bitter luck when the ball deflected off his shin and gave Aidan Nesbitt a chance to equalise in the 86th minute. However, his low angled drive lacked the height or the power to beat Jamie MacDonald.
Manager John McGlynn said afterwards: “We never really got into a comfortable position but I think it was well deserved. We were dominating without creating too much; at the same time, we denied Morton very much as well.
"It was kind of hard-fought, a bit of a grind – Morton were very well organised, disciplined and hard to grind down, so you have to keep plugging away, plugging away, plugging away. And it came.
"We might not have been at our silky soccer best but we deserved to win the game.”
Raith Rovers – J. MacDonald, Tumilty, K. MacDonald, Benedictus, Armstrong (Gullan 64), Hendry, Duku, Musonda, Tait, Ugwu (Vaughan 64), King (Matthews 69). Subs not used – Thomson (GK), Abraham, Spencer, Kennedy.
Greenock Morton – McAdams, Ledger, McLean, McGinty, McGinn, Nesbitt, Oliver (Orsi 73), Strapp, Lyon (Jacobs 64), Colville (McGuffie 83). Subs not used – Blues, Sterling.
Referee – John Beaton.