It was only their third win of that sequence, but in a complete performance, it came courtesy of a 55th-minute header from Collins who glanced home Paul Gallagher’s corner.
“It was a strong and determined performance,” said Wilson, whose side climbed back into the play-off places with the win.
“Yeovil had a few chances early on but we scrambled the ball clear and Mark (Howard) came to our rescue on a couple of occasions.
“But as the game progressed we looked strong and in control of defensive situations in particular.
“In front of goal we had a couple of instances where we perhaps should have done better, but the three points and momentum are paramount at this stage of the season.
“We saw last year how difficult it is to win here and it was as we expected, it was a keenly-contested match against a team who normally have a proud home record.
“We needed to roll our sleeves up today as we did against Doncaster, but we were exceptional at times in the second-half on Tuesday and didn’t get the credit we deserved.
“It was a different kettle of fish at Yeovil, the stadium is so tight and it is an intimidating place to come and play but we were resolute and got the all important goal to settle the contest.
“Of course there are areas to improve on as you would expect at this point in the season but we can look back on today as a job well done.”
The victory was the least United deserved. Prior to Collins scoring the only goal, the stand-in skipper had gone close to breaking the deadlock, as had Gallagher.
Yeovil Town: Stech, Ayling, Hinds, Webster, McAllister, Blizzard (Marsh-Brown 83), Upson, Smith, Hayter (Reid 69), Williams, Foley (Edwards 77). Unused substitutes: Stewart, Young, Ralph, Ugwu.
Sheffield United: Howard, McMahon, Maguire, Collins, Hill, Gallagher (Williams 80), McAllister, McDonald, Cresswell, Blackman, Kitson (Porter 64). Unused substitutes: Long, Westlake, Miller, Cofie, McFadzean.
Referee: R East (Wiltshire).
Man of the match: Paul Gallagher.