It was a fourth victory from five outings for the Blades, who remain unbeaten as they chase immediate promotion back to the Championship.
The visitors dominated midfield and were lively in attack but Yeovil defended doggedly - with too much determination at times as they picked up three bookings in the first half-hour at Huish Park.
It was always United who looked more likely and in the 41st minute they got the all important goal. Matthew Lowton hit a long ball from the right which Richard Cresswell controlled, he flicked it over a challenging defender and Porter helped it over the line.
Yeovil showed plenty of spirit in the second half, creating the better chances, but the Blades held firm. Steve Simonsen earned his money between the sticks with two good saves, one from substitute Anthony Edgar which temporarily slipped from his grasp.
The final drama came in stoppage time when Yeovil's Curtis Haynes-Brown was sent off for a second bookable offence - five minutes after being named Yeovil's man of the match.