Cole Stockton's second half header earned Tranmere their second home win in four days.
The half time substitute netted from close range for his fifth goal of the season - a strike that took Rovers back to the top of League 1.
Ronnie Moore opted for an unchanged starting XI following the 2-1 win over Crewe on Boxing Day.
A long range effort from Robbie Gibbons deflected wide of the target for Scunthorpe on four minutes and Ash Taylor produced a powerful header to clear the resulting corner.
Two deflections took the sting out of Michael O'Halloran's long range effort on 11 minutes while Andy Barcham side footed over the bar from 12 yards for the visitors seven minutes later.
Gibbons tried his luck from distance again on 29 minutes only for his shot to go over Owain Fon Williams' cross bar while Robinson curled a free kick over the top at the opposite end seven minutes later following good work from Ash Taylor.
Jake Cassidy headed a Robinson corner over the bar at the back post on 42 minutes, the final chance of the half.
The start of the second half brought the introduction of Cole Stockton in place of O'Halloran and the youngster was one of a number of players in the six yard box when Robinson's drilled cross was pushed away from goal by Mildenhall five minutes in. Despite none of them being able to react quickly enough for a shot, Rovers kept possession in the Scunthorpe half, winning a couple of corners in quick succession.
Two first time efforts from Max Power were blocked by the visiting defence and the Iron also repelled an effort from Cassidy on 57 minutes.
Rovers' pressure paid off on 59 minutes. Stockton won a corner on the right and after Taylor's powerful header was palmed up in the air by Mildenhall, Stockton was on hand to nod in from close range for his fifth goal of the season.
Taylor did well to clear a tricky cross from Barcham out of the Tranmere six yard box on 67 minutes after the Scunthorpe player had got past Bakayogo.
The visitors had a chance, albeit a difficult one, to level on 77 minutes. Fon Williams came off his line to punch a high ball clear of his area and with the keeper out of his goal it fell to Barcham who shot high over the bar from 25 yards.
Scunthorpe threw men forward late on - including their goalkeeper - but the Rovers defence held firm for a clean sheet and three points.
Tranmere: Fon Williams, Holmes, Taylor, Daniels, Bakayogo, McGurk, Palmer, Power, Robinson, Cassidy, O'Halloran (Stockton 45 HT). Substitutes: Mooney, Kay, Goodison, Black, Harrison, Thompson.
Scunthorpe: Mildenhall, Mozika, Canavan, Reid, Barcham, Hawley, Gibbons (Godden 73), Kennedy, Djeziri (Adelakun 73), Collins, Newey. Substitutes: Grella, Hughes, Wooton, Keegan, Slocombe.
Referee: Andy Davies
Yellow cards: Djeziri (45)