The Grecians were left to rue what could have been in a 2-2 draw with Bolton Wanderers on Saturday, while their hosts ran out 2-1 victors on Port Vale's turf.
Match preview
Masterminding his third away win as Shrewsbury manager, Paul Hurst - who took over from the sacked Matty Taylor towards the end of January - witnessed Daniel Udoh and Tom Bloxham bag the goals which would give the travelling crowd reason to celebrate against Port Vale on Saturday.
Seventeen-year-old Valiants attacker Baylee Dipepa gave the hosts a lifeline with just over 20 minutes of normal time remaining, but the teenager's first senior goal would be nothing more than a mere consolation, as Shrewsbury boosted their survival hopes at the expense of Port Vale's.
Thanks to an applaudable record of three wins from five away games since taking charge, Hurst has led the Shrews seven points clear of the relegation zone with nine matches of the regular season left to play, although the 49-year-old admitted that Saturday's triumph was far nervier than it should have been.
However, while the hosts have enjoyed most of their away days under Hurst so far, the Shrewsbury boss is yet to oversee a home victory for his new club, who have gone winless in their last six games at Montgomery Waters Meadow, losing five of them since beating Fleetwood Town 3-1 on New Year's Day.
In addition, the 17th-placed outfit have only mustered two goals across their six winless home affairs - failing to score in their last two against Wigan Athletic and Blackpool - and a paltry 28 strikes remains the worst attacking record in the 2023-24 League One campaign.
Thankfully for the Shrews, Tuesday's fixture sees them pit their wits against the second-worst offensive team in the English third tier, and Exeter City's 28th and 29th goals of the league season were not enough to propel them to a surprise success over promotion-chasing Bolton.
Trailing 1-0 at the break to a Paris Maghoma effort, Exeter's Sonny Cox left the Trotters shell-shocked with two strikes inside the first four minutes of the second half, but Eoin Toal met Jack Iredale's corner with a few moments of normal time remaining to force a four-goal stalemate.
Despite dropping two points in agonising fashion, head coach Gary Caldwell was still left "delighted" with a hard-earned draw against the former Premier League and UEFA Cup competitors, one which just about keep the Grecians above Shrewsbury in the bottom half of the table.
However, only goal difference is separating the two sides, and even then it is incredibly tight - Exeter's tally stands at -23 compared to Shrewsbury's -24 - and Caldwell's team are now without a victory in five matches, but three of their last four triumphs have come on the road.
Fireworks may not fly between the two evenly-matched teams on Tuesday, though, as the last two meetings have ended goalless, but Shrewsbury have triumphed in their last two home affairs with Exeter, netting seven goals across those 180 minutes of football.
Shrewsbury Town League One form:
D
L
W
L
L
W
Exeter City League One form:
W
L
L
D
L
D
Team News
Shrewsbury came out of the weekend's win over Port Vale without any new injury concerns to worry about, as Hurst confirmed that Jack Hinchy's withdrawal 10 minutes into the second half was tactical in nature; the Brighton & Hove Albion loanee is yet to complete 90 minutes in League One since his January arrival.
Left-back George Nurse is still on the long road to recovery from his cruciate ligament injury, while Roland Idowu, Joe Anderson, Nohan Kenneh and Ryan Bowman were not involved either.
Hurst reserved special praise for goalkeeper Marko Marosi after Saturday's game, and the Slovakian should line up behind an unchanged back four on Tuesday night.
As far as Exeter are concerned, long-term absentees Gabe Billington (ankle) and Demetri Mitchell (ACL) are not expected to play again before the campaign is over, and neither Will Aimson nor Ryan Woods were able to finish the draw with Bolton on Saturday.
The severity of their issues is currently unclear, but Cheick Diabate will slot into defence for Aimson if need be, while Reece Cole is eligible to take Woods's place in midfield after serving a two-game ban for picking up 10 yellow cards.
Shrewsbury Town possible starting lineup:
Marosi; Feeney, Dunkley, Sraha, Benning; Winchester, Perry; Bloxham, Bayliss, Shipley; Udoh
Exeter City possible starting lineup:
Sinisalo; Sweeney, Jules, Diabate; Niskanen, Carroll, Cole, Purrington; Harris, Aitchison; Cox
We say: Shrewsbury Town 1-1 Exeter City
For all of Shrewsbury's attacking shortcomings on home soil, Exeter arrive at Montgomery Waters Meadow with just one clean sheet from their last 14 away games and have often struggled to shut out their hosts on Salop soil.