Paddy Madden got the winner for the home side from the penalty spot, 15 minutes from time.
United went into the game unchanged from last week's 4-2 away success at Oldham Athletic.
So it was as you were in terms of the eleven, as Luke Daniels kept his place between the sticks, while Scott Wiseman, David Mirfin, Murray Wallace and Scott Laird made up the back four.
Jack King and Neal Bishop were the two central midfielders and the supporting trio to Tom Hopper remained intact, with Tommy Rowe, Gary McSheffrey and Madden playing in behind the frontman.
As expected, United were full of confidence after two wins on the bounce, and they started brightly. Rowe, who impressed in the win against the Latics, hit a dangerous strike two minutes in, which flew marginally past Shrews 'keeper Jayson Leutwiler's right hand post.
Despite the positive start, Mark Robins' men found themselves a goal down in the 15th minute. Sullay Kaikai picked the ball up around 25 yards from goal and then placed a low right-footed effort into the corner of Daniels' goal. The Iron shotstopper scrambled, but couldn't prevent the shot from creeping in.
The response was almost immediate, as Madden found room at the back post, but despite pulling the ball back in to a dangerous area, no one in claret and blue was there to tap home.
United continued to apply the pressure, this time it was McSheffrey who tried his luck and, after seeing his shot blocked, Rowe's effort was deflected over the crossbar for a corner kick.
15 minutes before the break came the Iron's best opportunity. The ball broke to Scotsman Wallace, who was all alone in the penalty area and it looked as though the net was destined to bulge, but his attempt was fractionally wide.
In spite of the fact that they were a goal ahead, the visitors weren't by any means resting on their laurels, and five minutes before the interval Tyrone Barnett stung the palms of Daniels with a sweetly struck shot from the edge of the box.
The early setback didn't seem to have a drastic effect on the amount of chances that United were creating, with Rowe dragging an effort just wide, moments after Barnett had seen his strike repelled.
They continued to probe, right up until the whistle, Laird it was this time who went close, with a deflected effort from the left hand side of box.
This was to be the last action of the first period, a period in which United created the better opportunities for sure.
Right from the restart, Robins' side took the game to the visitors, and two minutes in Laird almost drew the teams level. The full-back dropped his shoulder to get by Matt Tootle and then with the outside of his left foot forced Leutwiler into a smart save.
The former Preston man had an even greater chance minutes later, as the ball broke to him at the back post. However, he fired wide from close range.
It was a case of third time lucky for the Iron defender, as he equalised with a downward header at the far post. Madden picked out Laird superbly and much to the full-back's relief, he planted his header into the back of the net.
It could have so easily been 2-1 to the hosts when Hopper created some space for himself in the six-yard box, but the United frontman scooped his effort over the crossbar and into the Iron fans behind the goal.
The constant pressure paid off 15 minutes from time though, as Bishop was tripped in the penalty area and referee Eddie Ilderton had no choice but to point to the spot. Madden then stepped up and confidently placed the ball into the left corner of the goal, to give United a much deserved lead.
The visitors rallied late on, but none of their attempts were of any concern to Daniels, who was a spectator for the majority of the second half.
Despite the late pressure applied by Shrewsbury, Robins' side held on and in doing so made it three wins from three in League One.
Scunthorpe United: Daniels, Wiseman, Mirfin, Wallace, Laird, Bishop, King, McSheffrey (Lolley 60), Rowe (McAllister 88), Madden, Hopper (van Veen 60).
Substitutes not used: Anyon, Williams, Goode, Clarke.
Shrewsbury Town: Leutwiler, Black (Whitbread 56) Barnett (Whalley 77), Tootle, Collins, Knight-Percival, Cole (Akpa-Akpro 70), Kaikai, Brown, Smith, Ogogo.
Substitutes not used: Rowley, Sadler, McAlinden, Clark.
Attendance: 3,558 (227 away).
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