Shrews striker Liam McAlinden gave the hosts the lead five minutes before half time, and five minutes after the break, striker Tyrone Barnett rounded off the scoring, tapping into an empty goal.
Darren Kelly made five changes to his side from the weekend draw with Bury and he handed 18-year-old defender George Edmundson his professional debut at the heart of the defence.
Another one of those changes was goalkeeper David Cornell, and he was forced into early action, denying Barnett from the edge of the box.
The striker was played through on goal but the 24-year-old was equal to the effort and even got up to clear the rebound.
Latics started the game slowly and were almost punished two minutes later. Former midfielder James Wesolowski received the ball in space and shot but the goalkeeper was equal to the effort.
It was Cornell which was the more busier of the two goalkeeper’s and Barnett had another opportunity from Abu Ogogo’s pass. He knocked the ball beyond Cornell but Edmundoson was back to defend and clear the danger.
Latics did start to come back into the game and they started knocking the ball around comfortably but without purpose.
Midway through the first half came the first chance of the half for Latics. Saturday’s goalscorer Lee Croft received the ball on the right-hand side, he crossed to James Wilson, who was captain for the night, in the centre but defender Mark Ellis just nicked the ball from him at the last minute.
Croft was proving to be the source of Latics’ attack however his cross on the half hour mark into the centre was comfortably held by goalkeeper Jayson Leutwiler.
Barnett was causing the Oldham Athletic defence a problem or two and he won a free kick 25 yards from goal but Jordan Clark fired over the crossbar.
George Green had a sight of goal on 35 minutes for Latics but five minutes they found themselves behind in the game.
A loose ball in midfield was picked up by Shrews midfielder Clark and threaded a ball through to McAlinden who beat Cornell at his near post to put the home side ahead.
That goal came on 40 minutes and Shrewsbury had the chance to double their advantage just before the half time whistle.
Defender Ellis was left free at the back post but headed wide of Cornell’s post under little pressure from Latics’ players.
Seconds before the end of the half, it was Athletic who almost mustered an equaliser but Green’s sweetly-struck volley from 18 yards was saved by Leutwiler.
It was the former Everton man who almost equalised for Latics seconds into the second half.
The youngster put Shrews defender Jermaine Grandison under pressure, blocking his attempted clearance but it fell wide of Leutwiler’s goal.
However, two minutes later, the home side extended their lead through Barnett.
It was all Athletic’s own doing as they attempted to play the ball out from the back. Wilson’s backpass was short, picked up by Barnett who strolled past Cornell and stroked into an empty goal to double their advantage.
Latics needed a response and five minutes later they went almost had a sight of goal. Green picked up the ball in a dangerous area, picked out Turner who raced through with the goalkeeper but Shrews defender Grandison just got back to deny the striker.
Rhys Murphy was introduced into the action on the hour mark in place of Connor Brown as Latics switched to a 3-2-3-2 system.
That formation started to cause the home side a few problems as Green’s effort from 30 yards had to be turned past the post by the goalkeeper.
A minute later, Latics were adamant they should have been awarded a penalty as Murphy was barged into in the penalty area by Grandison but the referee waved play on.
Athletic introduced last season’s top goalscorer Jonathan Forte but struggled to calve open a stubborn Shrewsbury back line.
Clark and Junior Brown had shots for the home side but goalkeeper Cornell held on to both comfortably.
Approaching the end of the game, winger Yeates blasted a free kick over the crossbar as the game started to peter out.
Three minutes of additional time were signalled but Shrewsbury saw the game out comfortably and progressed to the second round of the Johnstone’s Paint Trophy.
Shrewsbury Town: Leutwiler, Grandison, Brown, Wesolowski (Lawrence 72’), Ellis, Ogogo, McAlinden (Whalley 68’), Knight-Percival (Sadler 78’), Clark, Barnett, Patterson.
Subs not used: Halstead, Akpa Akpro.
Oldham Athletic: Cornell, Dieng, Edmundson, Wilson, Brown (Murphy 61’), Jones, Philliskirk, Croft, Yeates, Green (Tuohy 84’), Turner (Forte 72’).
Subs not used: Coleman, Truelove.
Goals: Shrewsbury Town (McAlinden 40’, Barnett 49’) 2-0 Oldham Athletic
Attendance: 1,817 (133 visiting supporters)