With the starting XI already hit by injuries, United handed Nathan Stanton and Mark Jackson surprise starts despite not being at 100 per cent following recent injuries.
To cap it all off centre-back Cliff Byrne had to be replaced early in the match after suffering from exhaustion, while veteran winger Peter Beagrie could only make it to half time.
He had helped the Iron to a lead, but the home sides ability to bring on fresh legs saw them turn the match around in the closing stages and snatch an 82nd minute winner through defender Andy Lindegaard and end United's 14 match unbeaten run.
Iron manager Brian Laws said: "I think the exertions on Wednesday has caught us all up. They gave all they had but in the end we ran out of steam.
"I felt sorry for them because we just ran out of energy, they are absolutely shattered.
"I have no complaints about the defeat, but I'm disappointed for the players because they didn't deserve that."
Yeovil manager Gary Johnson was understandably pleased after seeing his side move up to 3rd in the Division Three table.
He said: "I was proud of my team and especially Lindy, he was certainly man of the match.
"I had to give them a bit of a shake up at half-time but they responded well."