Crawley Town rose up to 20th in League Two when Filipe Morais' second half goal earned them a valuable three points at Huish Park.
The victory edged Crawley towards securing Football League status for another season as it increased the distance between them and the relegation zone to nine points.
Reds left it late before finding the net as Morais' crucial winner was volleyed in brilliantly in the 72nd minute.
At the other end 'keeper Glenn Morris made sure of the three points by making three great saves in the closing stages to keep a clean sheet.
DID YOU READ?
Head coach Gabriele Cioffi named an unchanged side from last week's which lost to Forest Green Rovers.
Matty Willock and Luke Gambin came back into the squad returning from injury and were on the bench.
Glenn Morris made two useful saves in the first half hour to deny Alex Dobre and Ryan Seager in two attacks.
Reece Grego-Cox headed into the side-netting on the rebound after Panutche Camara put a ball into a good area from the wing.
Filipe Morais crossed to the far post to Ollie Palmer but there was not enough power on it and it flew well wide.
In the second half Reds set up a good chance when Tom Dallison combined with Lewis Young to find Palmer who didn't not get over the ball and shot well over the bar.
Yeovil went close with chances by Tristan Abrahams and Adel Gafaiti.
Cioffi brought on Nathaniel-George in place of Reece Grego-Cox, switching Filipe Morais to right while Nathaniel-George was on the left.
Nathaniel-George forced home 'keeper Nathan Baxter to make a fine save.
Willock then came on for Camara as Reds made their second substitution.
Morais earned Reds the lead in the 72nd minute when he fired first time a ball from Palmer into the back of the net.
Nathaniel-George went on a run looking for a second goal but the ball was cleared before he could shoot.
The Glovers pressed for an equaliser but were denied by Morris who brilliantly caught a headed effort by Seager from point-blank range at the second attempt.
Reds made their third substitution of the day by introducing Gambin off the bench for the last few minutes in place of Morais.
Morris helped clinch victory by making two great saves in quick succession during five minutes of added-time, keeping out two more good efforts by substitutes Alex Fisher and Sessi D'Almeida.
Crawley Town: Morris, Young, McNerney, Grego-Cox (Nathaniel-George 55), Palmer, Francomb, Maguire, Dallison, Bulman (capt), Morais (Gambin 87), Camara (Willock 66)
Unused subs: Mersin, N'Gala, Sesay
Yeovil Town: Baxter, Gafaiti, Warren (capt) (Pattison 68), Mugabi, Worthington, Duffus (Fisher 57), Abrahams, James, Dobre (D'Almeida 83), Ojo, Seager
Unused subs: Nelson, Gray, Rogers, John
Referee: Ben Toner
Attendance: 3,232 (141 away)