COLE Stockton's second-half header earned Tranmere their second home win in four days.
The half-time substitute scored from close range for his fifth goal of the season - a strike that took Rovers back to the top of League One.
Manager Ronnie Moore opted for an unchanged starting line-up 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.
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.
Scunthorpe threw men forward late on - including their goalkeeper - but the Rovers defence held firm for a clean sheet and three points.
Moore said: "We changed it at half time and changed the way we played from 4-4-2 to 4-3-3 like we did against Crewe and put Adam McGurk behind the strikers and it has worked for us.
"They had two big centre backs and they don't want pace, so that's why I'm a bit reluctant at times to have Cass and Cole in there together, but Cole did what all good strikers do, he got in there and sniffed it out.
"You have to grind out results sometimes, you can't be brilliant in every game.
"There were one or two tired legs out there but we kept going and kept going and if they were going to score it was going to be from a stupid free kick we'd given away or a corner. "
Rovers are away to Bury on New Year's Day and currently are top of the table with a tally of 47 points, one point ahead of second placed Sheffied Utd.