Town secured progression to the FA Cup second round as they beat York City 2-1 on Saturday afternoon.
Shrewsbury took the lead in the second minute after Tom Bayliss and Jordan Shipley linked up for the latter's fourth goal of the season.
Following a host of first-half chances, Town eventually doubled their lead in added time at the end of the first period from the spot when Luke Leahy converted.
However, York pulled one back instantly when Manny Duku headed home with seconds left of the first half.
Town boss Steve Cotterill went with a 3-4-1-2 formation at Montgomery Waters Meadow, with Christian Saydee partnering Rekeil Pyke up top.
It meant two changes from the side that battled its way to an excellent point at Portsmouth – with Pyke replacing Rob Street and Taylor Moore coming in for Elliott Bennett at right wing-back.
York, under the guidance of former Town boss John Askey, opted for a 4-4-2 system with Luke James and Duku the front two.
In a first half during which Shrewsbury created a host of chances, it took Town just two minutes to break the deadlock.
The move started with Saydee producing a lovely back heel that found the Bayliss. He then sent a low cross right into the danger area that was met by Shipley, who side-footed home from close range for his fourth goal of the campaign.
York tried to find an instant response with Ryan Fallowfield played in on goal only to be denied by a smart stop from Marko Marosi.
Town then saw Carl Winchester replaced as the midfielder limped off following a collision. He was replaced by Bennett.
From that point on, though, the chances kept coming for Steve Cotterill’s side.
They had a big opportunity to double their lead when Tom Flanagan made a surging run before finding Bayliss who then slipped Pyke through on goal.
The striker, though, was denied by Ethan Ross who raced off his line to make an excellent block.
Shrewsbury were on the attack again just moments later with Pyke this time turning creator.
The 25-year-old did well to hit the byline before delivering a cross that Saydee was inches away from side-footing home.
In the 19th minute, Bayliss, Shipley and Leahy combined well before Saydee hit a powerful shot from inside the box. But once again, Ross did magnificently to keep the score at 1-0.
After Town's relentless pressure, Salop had a corner which Leahy met at the back post. But Duku blocked his header just in front of the goal line.
Shrewsbury finally got the second goal their overall performance had deserved in added time at the end of the first half.
After Flanagan was brought down by Duku – referee Scott Tallis pointed to the penalty spot.
The resultant spot-kick was converted by Leahy – with the captain sending Ross the wrong way and finding the bottom corner.
However, just seconds before the break, York managed to drag themselves back into the game.
A cross from the left was met by Duku and he produced an intelligent header to nod the ball past Marosi.
Shrewsbury got their first chance of the second half in the 56th minute as Bayliss played a dinked pass to Leahy.
The captain then sent in a dangerous first-time cross but Pyke couldn’t quite get on the end of it.
Rob Street was close to securing his first FA Cup goal within four minutes of coming on.
Town played a long ball to Ryan Bowman who was able to cushion the ball and bring it down to lay off to Street but Ross made a great block.
Duku came close to achieving his second goal of the game 10 minutes before time as the striker rose highest in the Town box following Michael Duckworth's cross, but his headed ball sailed over the bar.
Leahy came so close to securing victory for Shrewsbury in added time at the end of the match after Tom Bloxham burst into the box. The striker delivered a cross that was deflected to Leahy, but his effort didn't find its way through the crowd of York bodies.
Fortunately, Town didn't need that chance to secure victory as their solid performance throughout the 90 minutes paid off as they secured their place in the hat for the FA Cup second round.
Marosi (GK), Leahy (C), Pennington, Moore (Bloxham, 79), Winchester (Bennett, 9), Pyke (Bowman, 60), Bayliss, Dunkley, Saydee (Street, 60), Shipley, Flanagan
Burgoyne (GK), Caton, Barlow
Ross (GK), Fallowfield (Dyson, 72), Kerr, Kouhyar, Whittle (Hancox, 82), Sanders, Pybus, Mafuta, James, Duku, Duckworth (C)