The two League One sides were both forced to negotiate penalty shootouts to seal their spots in the second round.
Match preview
Shrewsbury may be in the EFL Cup second round, but they have experienced a difficult start to the season, having failed to win any of their first five competitive matches in regulation time.
After losing 1-0 to Stevenage in their league opener, Paul Hurst's side went on to play out an entertaining 3-3 draw in their EFL Cup tie with Notts County before winning the subsequent penalty shootout.
The Shrews were unable to build upon their penalty shootout success, having gone on to lose three consecutive matches in all competitions, including league defeats to Peterborough United and Huddersfield Town.
Those two losses have extended Shrewsbury's winless league to 10 matches, leaving them waiting for their first win in League One since beating Carlisle United in March.
They may welcome the distraction of an EFL Cup tie, especially as they have the chance to reach the third round for the first time since 2014-15.
Bolton have made a mixed to the new League One season, collecting four points from two matches before losing to Charlton Athletic on Sunday.
Charlton's Greg Docherty and Matty Godden grabbed a goal apiece to condemn Ian Evatt's side to their first defeat of the season and their away league loss since March 16.
The Trotters will look to get their league campaign back on track in Saturday's home clash with Exeter City, but first, they must negotiate an EFL Cup clash with Shrewsbury.
After beating Mansfield Town on penalties in the first round, the Trotters are looking to reach the third round for the first time since 2017-18.
However, their hopes of reaching the next stage may be tempered by the fact they have been eliminated in the second round in each of the last three seasons.
Shrewsbury Town EFL Cup form:
W
Shrewsbury Town form (all competitions):
L
W
L
L
L
Bolton Wanderers EFL Cup form:
W
Bolton Wanderers form (all competitions):
W
W
D
L
Team News
Shrewsbury are expected to be without the injured trio of Jordan Rossiter and Josh Feeney due to knee and hamstring injuries.
Harrison Biggins and George Lloyd dropped down to the bench at the weekend, but they could be considered for recalls for Tuesday's EFL Cup clash.
As for the visitors, they are expected to be without the services of Gethin Jones and Randell Williams due to injury.
Jordi Osei-Tutu and Victor Adeboyejo are in contention to start after featuring as half-time substitutes at the weekend.
Evatt is likely to make further changes to freshen up his side, with Luke Southwood, Chris Forino-Joseph, Jay Matete and Scott Arfield among those who could be considered for Tuesday's contest.
Shrewsbury Town possible starting lineup:
Savin; Hoole, Nsiala, Pierre, Benning; O'Reilly, Biggins, Winchester, Shipley, Bloxham; Lloyd
Bolton Wanderers possible starting lineup:
Southwood; Forino-Joseph, Santos, Johnston; Osei-Tutu, Matete, Sheehan, Schon; McAtee, Collins, Adeboyejo