Luke Wilkinson's emphatic finish following Craig Alcock's throw-in was enough to secure victory for the visitors
After a cagey first half, the game came to life in the second as Wilkinson hammered his second goal for the club and put the visiting green and whites ahead.
The goalscorer's afternoon took an unexpected turn after goalkeeper Liam O'Brien's injury, Wilkinson was forced to play in goal, making a stunning save in stoppage time.
Despite the hosts continual pressure following the goal, they could not break down a resiliant Yeovil back-line as the three points would head down the M5 to Huish Park.
Darren Sarll made two changes to the side which was victorious over AFC Fylde, one of which being enforced upon him.
After taking a knock in training, Remeao Hutton was not included in the matchday squad and replaced by Craig Alcock.
Jimmy Smith was the second of the changes as he replaced Brighton loanee James Tilley for his first competitive start for the club after netting in last weekend's win.
A long throw-in in the second minute saw the first chance of the game fall to the hosts, Adi Youssuf rose highest but the Solihull forward had his headed effort cannon off the crossbar.
Yousuff looked lively in the opening proceedings registering the first shot on target in the 10th minute from the edge of the box which was easily stopped by Yeovil goalkeeper O'Brien.
The Glovers would find routes in-behind the Solihull back four with ease when they pushed forward. Rhys Murphy was the first in the 11th minute as he twisted and turned his way to the byline, but his pass across the goalmouth couldn't find Gold Omotayo.
A driving run from Charlie Lee won Town a free kick in the left channel in the 15th minute. Murphy attempted to replicate his goal against AFC Fylde but the enrushing Solihull defence was able to turn the ball wide.
Solihull Moors won their first free-kick in a shooting position after a trip by Lee on Jamey Osbourne as he drove towards goal. Osourne would take the free kick but his effort was well over the bar.
Yeovil almost had the goal of the season competition wrapped up by mid-September as a stunning Myles Hippolyte flick sent the ball into the path of Jimmy Smith. The midfielder found Omotayo in the box but his effort fell to Murphy who was stood in an offside positon.
The Glovers would go inches away from taking the lead as Hippolyte in the 27th minute struck a volley from the edge of the box. The forward-thinking midfielder managed a clean connection but his effort had too much power and shot over the bar.
Just one minute later, Osbourne would go close with a similar effort to Hippolyte's as Yeovil struggled to clear their lines, he struck a volley from 25-yards out which flew wide of the goal.
Chances would come thick and fast as the half came to a close with Matt Worthington hammering an effort first time from 20-yards out, which flew narrowly over the bar.
The best chance of the half would fall to the Glovers in the 34th minute. Despite having Lee down with a facial injury, the referee allowed play to continue, the ball would be clipped into the box and met by Omotayo who has his acrobatic effort saved by Ryan Boot.
Solihull managed to create their first route in behind in the 39th minute. Lee Vaughan would be sent through in the right channel but his effort from a tight angle is easily stopped by O'Brien.
The hosts' best chance of the half would be the last action of the first period as Terry Hawkridge found space on the right wing. The wide-man played a perfectly weighted cross to the back post to find Reckord but the full back could not direct his effort on-target.
Neither side were able to gain a significant stranglehold of the game by half-time with the score still goalless at the break.
As the second half began, it would only be a matter of minutes befire Omotayo would have the first chance of the half. The tall striker made his way inside the Solihull box and fired on-goal but his effort was easily collected by Boot.
The Glovers would finally take the lead in the 58th minute, after Craig Alcock's throw, the ball fell nicely to Omotoayo, after his first effort was blocked, Wilkinson powered through bodies and fired home to send to Yeovil Town a goal ahead.
Solihull would not find themselves disheartened by going a goal behind creating a number of chances quickly after. The best of these fell to Danny Wright who powered beyond the Glovers defence but had his effort saved by O'Brien.
As time ticked on, Solihull began to mount more pressure on the Glovers backline. The hosts would go close after substitute Albi Skendi gave away free-kick in a shooting position. Osbourne took the set-piece but his strike to a knick off the wall.
The hosts continue to push as the second half progressed, O'Brien was forced to produce some excellent saves to keep them at bay. The pick of the bunch was following saving Osbourne's effort from distance, the shotstopper reacted quickly to deny Danny Wright from close range.
The Moors pressure was relentless as substitute Darren Carter going close with an effort from the right-hand side of the box.
In the dying embers of the game, an injury to O’Brien forced the goal scorer Wilkinson to end the game as a goalkeeper.
Wilkinson would be forced into a stop as he acrobatically denied Wright with a brilliant dive to tip the ball wide at the back post.
With ten men on the pitch, Yeovil battled valiantly in the final moments to secure a fifth victory in a row.
Solihull Moors: Boot (GK), Reckord (Nicholls 85), Storer ©, Daly, Gudger, Osborne, Hawkridge (Carter 71), Wright, Vaughan (Neufville 79), Howe, Yussuf.
Subs not used: Hancox, Rowley.
Yeovil Town: O'Brien; Alcock, Dickinson, Wilkinson, Collins; Lee (D'Ath), Worthington, Hippolyte (Tilley), Smith (Skendi); Murphy, Omotayo.
Booked: Lee, Hippolyte, Wilkinson.
Subs not used: Bradbury, McCoy.