Boss Sam Ricketts got the response he wanted from his players after last week's home disappointment against Fleetwood as Town proved too good for Micky Mellon's 10-man Rovers in a fixture that was more comfortable than the 1-0 scoreline suggests.
Town reporter Lewis Cox rates the performances.
Max O'Leary - Probably his most memorable outing in Town colours and definitely saved his side two points at Prenton Park. The save from Neil Danns deep into added time sticks in the memory but denying Stefan Payne was just as impressive. A commanding presence too. Showed his prowess. 7
Ro-Shaun Williams - Solid. Generally looked after the ball really well over short and long distances and was a good presence in the air. Former team-mate Payne was Tranmere's only threat and Williams did well. 7
Aaron Pierre - Back in the starting line-up and looking like he had not been away. The Grenada skipper was dominant in the air and looked sharp on the ground. Took his first Shrewsbury goal with aplomb. He is certainly a threat in attacking areas and almost had another. Some super defending too. 8
Omar Beckles - Another good performance from the defender, who played on the left side of the back three. Seemed to be targeted by balls over the top early on but dealt with them well. Made one crucial interception. Unlucky with a volley. 7
Donald Love - In what is becoming something of a trend the right-sided defender but in another solid if unspectacular display. His use of the ball, particular over distance, was generally good. And no worries about his engine getting up the field. Defensively sound. 7
Ollie Norburn - Big day for the Town skipper back at the club he helped to Wembley glory two seasons ago and he shone for Shrewsbury. Set the tone early on by winning big challenges and was very good on the ball. Should've netted but was unlucky to hit the post. Mature display from the leader. 8
Sean Goss - A little quieter than in other games but still influential for Shrewsbury. Didn't seem to have the ball as much as he has in previous games but his dead balls were still a superb asset for Town and really troubled the hosts. 7
Josh Laurent - An absolutely tireless display from the midfielder who is so key at setting Town's energy levels as a team. He presses brilliantly and causes problems. When others tire Laurent continued to run and was at the heart at a lot of the second-half chances. 7
Ryan Giles - The teenager looked the sharpest he has for a little while doing well in both directions up against the lively right-back Jake Caprice. Giles' delivery continues to be his standout trait with some on-the-money crosses and a good low strike tested the keeper. 7
Callum Lang - Not for the first time since his arrival a little over a month ago the striker was one of Town's shining lights. His attitude and work rate is a joy to behold and it was good to see him sniffing out the goal for Pierre's winner after missing a decent chance. Knock to his ankle late on. Hope he's OK. 8
Daniel Udoh - Handed his second Shrewsbury League One start, a nod to how much the former Telford man is catching the eye. He is another whose attitude is infectious and, while there were some raw moments, he did not stop. Carries a threat too, with his pace and power. 7
Fejiri Okenabirhie (Lang, 70) - Great to see him back from injury. A couple of efforts could've gone in on another day. 6
Louis Thompson (Udoh, 83) - Ditto Okenabirhie. Can become an important midfield option. Good running late on. n/a
Brad Walker (Norburn, 90+3) - n/a
Subs not used: Murphy, Edwards, Whalley, Cummings.