An own goal by Shrews defender Oliver Lancashire set the hosts on their way in the opening period, with the victory being rounded off by debutant Jonathon Margetts in the second half.
There were eight alterations to the Scunthorpe line-up which defeated Bury at the weekend. Included in those changes was Levi Sutton, who took the place of Scott Wiseman, in his first start for the club.
Inside the first minute, United went close to getting themselves in front, when Kevin van Veen struck a powerful shot from just outside the box. Shrews ‘keeper Mark Halstead foiled him though, and grasped his attempt.
Seven minutes later however, the hosts dealt the first blow. After he’d picked up the ball on the left, Conor Townsend drilled a cross into the near post, where defender Lancashire was the unlucky man, as he turned the ball into his own net.
Ivan Toney went within inches of squaring things up moments later but, despite beating Joe Anyon, his shot rattled the post, and bounced clear of danger.
Van Veen would have been disappointed not to have doubled the Iron’s advantage ten minutes before the break as, after being found unmarked at the near post, he could only manage to glance his header over the crossbar.
The visitors’ best opening came not too long after the Dutchman had missed the target. Anyon initially did well to deny Toney, resulting in the ball dropping for Antoni Sarcevic, who blazed over from close range.
Chances were aplenty it seemed ahead of the interval, with Paddy Madden the next to register an effort on goal. Sutton firstly did superb to slip the Irishman in, as he then forced Halstead into a fine save with his feet.
The save was the last act of the first half, with the Iron going one ahead at the break.
Micky Mellon’s men seeked a quick response after the restart, and they thought they’d got one when Sarcevic stabbed home at the far post. The celebrations were cut short however, as the linesman’s raised flag confirmed the Shrews man was stood in an offside position.
First half substitute Margetts then went close to opening his Iron account with a snapshot from a tight angle. Halstead was up to it though, and pushed the ball away to safety.
He wouldn’t be frustrated for too much longer though and, in the space of four minutes, the striker did manage to find the back of the net. Credit to Sutton, who did superbly to lay the ball on a plate for the former Lincoln City man, who did the rest, and headed home from virtually on the goal-line.
That second Scunthorpe goal looked as though it’d open the floodgates. Van Veen was keen to get a piece of the action, but his nonchalant chip drifted just wide of the goal, following a strong run from the striker.
Toney, who’d hit the post with an earlier free kick, then went even closer to getting on the scoresheet, but he was again denied, this time by Anyon, who reached up to tip the ball over the crossbar and out for a corner.
Mellon’s side then had another strike chalked off, again for offside. On this occasion it was substitute Andy Mangan who was the unfortunate party, as he saw his close range finish was ruled out.
Nothing was getting past Anyon, as he then made three saves to frustrate firstly Ian Black, Jim O’Brien, and finally Toney, whose powerful strike stung the palms of the United stopper.
In truth, United never really looked like conceding throughout the 90 minutes, and they deservedly progressed to the next phase of the competition, as they played out the remaining minutes with relative ease.
Scunthorpe United: Anyon, Wallace, Dawson (Adelakun, 46), Madden, van Veen, Hopper (Margetts, 24), Mantom, Goode, Townsend, Ness, Sutton.
Substitutes not used: Kelsey, Wiseman, Mirfin, Holmes, Sithole.
Shrewsbury Town: Halstead, Grimmer, Toney (Leitch-Smith, 89), El-Abd, O'Brien, Brown, Sarcavic (Waring, 62), Deegan, Lancashire, Black, Choulay (Mangan, 46).
Substitutes not used: Leutwiler, Sadler, Roberts.