In a first half devoid of clear-cut chances the Glovers held their own against the third division promotion hopefuls to go in level, teeing up a winner takes all second 45 after the restart.
With the stakes upped after the break both sides registered shots on target, before Carlton Morris broke the deadlock just past the hour-mark.
The Green & Whites almost caused a dramatic ending when Otis Khan was brilliantly denied by the home stopper, but it wasn’t to be as Shrewsbury progressed to the final.
Targeting a national cup final for the first time since 2002, Darren Way made five changes to the side that lined up against Carlisle United last time out.
Without Lewis Wing, Ryan Seager (both ineligible) and Jake Gray (ankle), Connor Smith, Francois Zoko and Khan came into the starting eleven as the Glovers switched to a 4-3-3.
With Sam Surridge and Rhys Browne dropping to the bench, Jared Bird and Jordan Green completed the alterations for the trip to Shropshire.
Having waited an additional week to play for the chance to walk out at Wembley due to the initial postponement, both sides started in determined fashion.
Just two minutes were on the clock when Salop’s quick counter-attack ended with Jon Nolan blazing over from inside the box, before Khan saw a curling effort deflected over the bar at the other end in an immediate response from the visitors.
Settling into a less frenetic affair past the 10-minute mark, it became an intriguing tactical battle between the two managers who completed the UEFA A License together.
With neither side able to claim a monopoly on possession both teams traded spells of pressure with Khan particularly lively on the left wing, but it became a relatively cagey affair with both goalkeepers relegated to being merely spectators.
Unable to find a way to call Jonny Maddison into action Ben Godfrey’s wayward first-time strike was as good as it got for Paul Hurst’s side, whilst Jordan Green’s tame header was the only attempt on target in the opening 45 minutes of action as Town matched their high-flying League One counterparts.
In a bid to grab more of a foothold in the tie in the second half, Way made two substitutions in quick succession as Surridge and Browne replaced Gobern and Green in a reshuffle to a 4-4-2 formation.
However, it was Salop who created the first chance after the restart when Shaun Whalley’s volley at the back stick flashed wide of Maddison’s far post.
The winger’s attempt sparked a flurry of attacking activity as the game opened up towards the hour-mark with chances at both ends.
Nolan stung the hands of Maddison from range for Shrewsbury, a chance sandwiched between Khan and Zoko firing into the arms of Dean Henderson.
With the game opening up, the hosts took advantage with 63 minutes on the clock.
Whalley’s inswinging corner was tantalising, rousing the attention of Morris who rose highest in the middle to head home the opener.
Boosted by the home fans in full voice Hurst’s side looked to turn the screw in the immediate aftermath following the goal, but Town rode out the danger to setup a tense final 10 minutes.
Looking to continue their perfect record against League One opposition this season the visitors threw caution to the wind in the dying embers of the match and almost forced a penalty shootout in additional time.
The Glovers stormed forward in numbers and Browne’s neat through ball found Khan on the angle, but his poked effort was brilliantly kept out by Henderson as Salop held on to book a spot at Wembley.
Shrewsbury Town: Henderson; Godfrey, Nsiala, Sadler, Beckles; Nolan (John-Lewis 90′), B. Morris, Ogogo; Whalley, C. Morris (Payne 81′), Rodman (Thomas 70′).
Bookings: Whalley 87′
Subs not used: MacGillvray, Lowe, Gnahoua, Eisa.
Yeovil Town: Maddison; Whelan, Sowunmi, James, Dickson; C. Smith, Gobern (Surridge 46′), Bird (Santos 73′); Green (Browne 50′), Zoko, Khan.
Bookings: James 21′, Khan 57′
Subs not used: Phillips, Mugabi, Donnellan, Fisher.
