That came after just seven minutes when the Croatian latched on to Fernando Ricksen’s cutback to nod a looping header beyond the grasp of Derek Stillie and it looked for a while as if that early strike would inspire Rangers to pour forward to try to bolster their goal difference with further goals.
Some poor finishing, however, left the game in the balance for the duration of the match and the sound of the vast travelling support urging referee Kenny Clark to blow for the final whistle told its own story.
The win drew Rangers to within two points of Celtic ahead of the crucial Old Firm game at Ibrox next Sunday, a match that could go a long way in deciding the destination of the SPL championship.
McLeish must lie awake at night wondering how his side could cope should the fates conspire to ever deny him the services of Prso.
The impressive Croatian was again Rangers’ best player, his tireless running and nimble footwork earning him a standing ovation from the visiting supporters spread over three-quarters of the stadium.
He came close to adding a second goal after the break with a clipped effort from a tight angle that Stillie clawed off his line and then, to prove he was human after all, mis-controlled Gregory Vignal’s through ball after beating the offside trap.
By that time though Rangers should have already had the three points all wrapped up.
It would prove to be yet another fruitless afternoon for Prso’s strike partner, Nacho Novo, looking for his first league goal since March 2.
After missing a few decent chances in the surprise defeat to Dundee United in the previous game, the Spaniard was unable to end his current scoring drought against a limited Dunfermline side.
The most clear-cut opportunity came with 23 minutes played when he latched onto Gary Mason’s poor passback but could only slide a tame effort wide of goal.
He was later substituted on the hour mark – to be replaced by Shota Arveladze – and the manner in which he trooped off the pitch with his head down said more than words ever could.
Missed chances cost Rangers three valuable points against United five days earlier and when Thomas Buffel poked a simple chance wide of goal after good work from Ricksen you began to fear a repeat was on the cards.
Dunfermline, battling to avoid the drop into the First Division, took heart from Rangers’ inability to capitalise on promising opportunities to launch a few attempts of their own.
Noel Hunt should have done better than thump a half-volley wide of goal after controlling a cross on his chest at the back post before Darren Young clattered Ronald Waterreus’ post with a fierce drive.
With the goalkeeper stranded, Hunt hurriedly rushed the rebound attempt and sent it high into the stand.
At the back, Sotirios Kyrgiakos and Bob Malcolm both produced solid performances at the heart of the Rangers defence.
Malcolm, in particular, cut a commanding figure, towering over strikers Georgi Hristov and then substitute Jesper Christiansen time and time again to nullify Dunfermline attacks at source.
As play descended into a series of niggling fouls, bookings and substitutions, Rangers seemed content to hold onto their slim lead with their opponents lacking the nous to offer any real threat at the other hand.
A counter attack led by Vignal in the closing minutes left the Light Blues with three-on-one but the Frenchman chose to ignore his team-mates and instead go for glory but thrashed an effort tamely into the side netting.
The final whistle shortly after brought proceedings to an end, leaving Rangers with all three points but with much to contemplate before Celtic come calling next weekend.
RANGERS (4-4-2): Waterreus; Ross, Kyrgiakos, Malcolm, Ball; Buffel (Namouchi 79), Ricksen, Ferguson, Vignal; Prso, Novo (Arveladze 60)
Subs: McGregor, Khizanishvili, Burke, Thompson, McCormack
Booked: Prso (66), Buffel (78)
Dunfermline (4-4-2): Stillie, Skerla, Wilson, Thomson, Campbell, Hunt, Darren Young, Mason, Derek Young, Donnelly (Mehmet 63) Hristov (Christiansen 76)
Subs: Langfield, McKeown, Wilson, Scullion, Ross
Booked: Stillie (40), Skerla (48), Campbell (66), Young (90)
Man of the Match: Dado Prso