The Glovers scored either side of half-time courtesy of Ryan Hedges and Otis Khan, before Town were reduced to ten men when Kevin Dawson was sent-off for a second bookable offence after 54 minutes.
Making the most of their numerical advantage, Jack Byrne scored twice in quick succession to level the scores, forcing a replay and a trip to Damson Park for Yeovil.
Darren Way made three changes to the side that extended the Glovers unbeaten run in Sky Bet League Two to four matches last time out against Grimsby Town, with Liam Shephard and Tom Eaves replacing Bevis Mugabi and Tahvon Campbell respectively. Elsewhere, Ben Whitfield came into Town’s midfield in place of the injured Alex Lawless.
One notable change on the bench saw new signing Daryl Allinson take a seat amongst the substitutes, with the 13-year-old signing on at Huish Park earlier this week having impressed manager Way with his resilience and bravery when battling a rare form of leukaemia.
Looking to avoid an Emirates FA Cup upset, the Glovers immediately came out on the front foot, with Whitfield’s rasping effort from 20 yards stinging the fingertips of Moors ‘keeper Danny Lewis after just three minutes.
Looking to find an early lead Otis Khan glanced a pinpoint Kevin Dawson wide of the target, before the hosts took the lead after eight minutes.
Neat build-up play between Eaves, Dawson and Hedges resulted in the Swansea-loanee finding space in the box, smashing a driven effort past a hapless Lewis from 10 yards after his initial attempted cross was blocked.
Buoyed by taking the lead, Town pressed for a second and almost netted three minutes later in what would’ve been fortuitous circumstances.
Nathan Smith’s attempted cross looped goalwards before nestling on the roof of the net to the relief of a scrambling Lewis in the Solihull goal.
The National League ‘keeper was called into action again just before the half-hour mark, this time to save smartly with his legs to keep out Whitfield’s low shot from 12 yards after neat build-up once again.
After a ferocious start the Glovers became increasingly frustrated by Solihull’s defensive tactics which saw 10 players deployed behind the ball, with the National League outfit rarely threatening Artur Krysiak in the Town goal.
Moors midfielder Jamie Osborne forced a comfortable save with an audacious 30-yard effort, before the visitors failed to capitalise on a number of set-pieces in threatening positions before the break.
After an impressive start to the first half, the Glovers repeated the feat in the second immediately calling Lewis into action in the visiting goal.
Eaves found space in the box before forcing Lewis into a smart save from the angle, before the Moors ‘keeper produced a stunning low save to tip Matty Dolan’s effort from 20 yards onto the post.
Yeovil looked determined to extend their lead at Huish Park and did so six minutes after the restart, doubling their lead in sublime fashion.
After Whitfield was fouled 25 yards from goal, Khan stepped up and dispatched the free-kick into the top corner leaving Lewis with no chance.
At 2-0 the Glovers looked to be coasting, but the hosts were dealt a blow when Dawson received his marching orders for a second bookable offence with 35 minutes left to play.
Sniffing the chance of a comeback with their man advantage the visitors clawed a goal back just before the hour mark through Byrne.
After ricocheting around the box the Solihull midfielder was on hand to fire an effort past Krysiak from just inside the box, as Yeovil waited to introduce Mugabi into the mix.
With the score at 2-1 Way introduced the defender with Shephard pushing forward into midfield to fill the gap left by Dawson, but Moors stunned the home faithful by drawing level after 63 minutes.
From a Connor Franklin long throw the ball fell again to Byrne, who in similar circumstances to his first goal drew the National League outfit level.
Way switched the Glovers formation to a 4-3-2 with Francois Zoko replacing Khan to partner Eaves up front, a switch that went some way to nullifying the immediate threat offered by Marcus Bignot’s side.
As the game entered the final 10 minutes Jamie Osborne fired an effort over the bar for the visitors, whilst Shephard curled an effort over the bar from 20 yards.
With a replay in the offing, Eaves had the ball in the net for the Glovers only to be denied by the linesman’s flag, before Dolan flashed an effort from 25 yards just wide in additional time at the end of the match.
After an all-action second half neither side could find a winner, forcing an Emirates FA Cup First Round replay where the Glovers will travel to Damson Park for a spot in the Second Round.
Yeovil Town: Krysiak; Shephard, Ward, Lacey, Smith; Dawson, Dolan, Whitfield (Mugabi 57’); Hedges, Eaves, Khan (Zoko 69’).
Bookings: Dawson 31’, 54’ (sent off), Mugabi 81, Shephard 89’.
Subs not used: Maddison, Allinson, Ezewele, Dickson, Sowunmi, Campbell.
Solihull Moors: Lewis; Jones (Asante 76’), Fagbola, Daly, Gough, Franklin; Murombedzi, Byrne, Osborne; White (Sterling 76’), Brown.
Subs not used: Koue-Niate, Vaughan, Hayden, Dielna.