Callum McFadzean's goal means Sheffield United will take a one-goal lead into the second leg of their League One play-off semi-final against Yeovil.
The Blades felt they should have had a penalty when Barry Robson seemed to be elbowed by Jamie McAllister.
However, United went ahead just after the break when McFadzean's shot from 12 yards went in after a deflection.
George Long produced an excellent reaction save to deny Byron Webster an acrobatic last-minute leveller.
McFadzean's fine start
Sheffield-born McFadzean's effort against the Glovers was his first senior goal. The 19-year-old's brother, Kyle, plays for League One Crawley.
The Blades, who lost last year's League One play-off final 8-7 on penalties to Yorkshire rivals Huddersfield, entered the play-offs with the unenviable record of six attempts and no promotions.
They had failed to score in their previous three matches leading up to this encounter but went close when the returning Robson flashed a free-kick just past the post.
That was as close as either side got in a first-half that was high in effort and energy but lacking in real clear-cut chances, while Robson went off injured and was replaced by McFadzean.
Given the frenetic nature of the first-half it was something of a surprise that the deadline was broke within seconds of the restart.
Chris Porter got in behind the Glovers defence to lay-off for Jamie Murphy whose cutback into the area came to McFadzean and his shot beat keeper Marek Stech via a deflection that went in off the post.
Yeovil, who had relied on counter attacks started by Stech before the break, responded well and James Hayter chipped in from a marginally offside position.
McFadzean came close to doubling the advantage for Chris Morgan's side after a clever run from the wing culminated in him firing straight at Stech before Murphy went close after drifting inside from the opposite side.
For the visitors 22-goal Paddy Madden was finding it hard to escape the attentions of Blades centre backs Harry Maguire and Neill Collins and on the one significant occasion he did, the latter was there to clear his header off the line.
Long was forced into late action from Webster's close-range overhead kick but the Blades held out.
They travel to Huish Park on Monday hoping to reach a fifth play-off final but Yeovil boss Gary Johnson will have been encouraged by the endeavour shown by his side.
VIEW FROM THE DRESSING ROOM
Sheffield United caretaker-manager Chris Morgan told BBC Radio Sheffield:
"I thought we were excellent. Yeovil put us under a lot of pressure late on, which you'd expect.
"We had a game plan and we stuck to it. We knew it was going to be tight on the night and we're pleased with a 1-0.
"We're strong away from home as well. They know what our away record is like."
Yeovil manager Gary Johnson:
"If we can be a bit better and take our chances on Monday then of course we're still well in it.
"I thought defensively we were fantastic because we had to deal with a bombardment into our box.
"We'll be up for it again and I know the Yeovil Town fans will be right up for it, it's a tight ground at Huish Park and I think it will be a cracking game.
"Me and the boys feel Monday can't come round quick enough."
- 25 Long
- 02 Westlake
- 05 Maguire Booked
- 06 Hill
- 15 Collins
- 08 Doyle Booked
- 11 McDonald
- 19 Robson (McFadzean - 31' )
- 09 Porter (Whitehouse - 90' )
- 14 Kitson Booked (Ironside - 74' )
- 23 Murphy
- 35 Coyne
- 04 Higginbotham
- 33 Barry
- 21 Chapell
- 26 McFadzean
- 27 Whitehouse
- 24 Ironside
- 01 Stech
- 02 Ayling
- 03 McAllister Booked
- 05 Webster
- 18 Burn
- 20 Edwards
- 08 Upson
- 14 Foley
- 22 Dawson
- 09 Hayter (Balanta - 73' )
- 17 Madden
- 12 Stewart
- 04 Hinds
- 13 Maksimenko
- 06 Blizzard
- 10 Williams
- 15 Young
- 29 Balanta
Live Text Commentary
Full Time The match has reached full-time.90:00 +4:15
Centre by Jamie Murphy.90:00 +3:13
Byron Webster concedes a free kick for a foul on Joe Ironside. Direct free kick taken by Neill Collins.90:00 +1:42 Substitution
Substitution Chris Porter leaves the field to be replaced by Elliott Whitehouse.90:00 +1:08
Inswinging corner taken by James McAllister from the right by-line, Byron Webster has a header from deep inside the six-yard box and clears the crossbar.90:00 +1:08 Booking
Booking Harry Maguire receives a caution for unsporting behaviour.89:57
Darryl Westlake challenges Sam Foley unfairly and gives away a free kick. James McAllister delivers the ball, Byron Webster takes a shot. Save made by George Long.88:43
Shot from just outside the area by Edward Upson goes over the bar.88:35
Centre by James McAllister, clearance made by Harry Maguire.88:24
Paddy Madden produces a cross, Harry Maguire makes a clearance.86:54
The assistant referee signals for offside against Kevin Dawson. George Long takes the free kick.85:54
Joe Ironside takes a shot. Marek Stech makes a save.85:12
Inswinging corner taken right-footed by Darryl Westlake from the left by-line, clearance by Dan Burn.84:29
Paddy Madden is ruled offside. Harry Maguire takes the free kick.83:45
Luke Ayling crosses the ball, save made by George Long.83:28
James McAllister delivers the ball, clearance by Neill Collins.83:18
The ball is sent over by Paddy Madden.82:15
Luke Ayling fouled by Matthew Hill, the ref awards a free kick. Free kick taken by Marek Stech.81:13
The ball is delivered by Darryl Westlake, Marek Stech makes a save.80:02
Edward Upson takes the inswinging corner, Byron Webster takes a shot. Brilliant save by George Long.
Corner taken left-footed by James McAllister from the right by-line, Harry Maguire manages to make a clearance.79:17
Luke Ayling crosses the ball, Callum McFadzean manages to make a clearance.78:19
Free kick awarded for an unfair challenge on Jamie Murphy by Sam Foley. Darryl Westlake delivers the ball, Harry Maguire takes a shot. Clearance by Dan Burn.76:04
Shot from just outside the penalty box by Michael Doyle misses to the left of the target.73:32
Direct free kick taken by Matthew Hill.73:32 Substitution
Substitution Joe Ironside is brought on as a substitute for Dave Kitson.73:32
Luke Ayling challenges Dave Kitson unfairly and gives away a free kick.72:26
Corner taken left-footed by James McAllister, Neill Collins manages to make a clearance.72:26 Substitution
Substitution Angelo Balanta is brought on as a substitute for James Hayter.71:46
The ball is delivered by Luke Ayling, Paddy Madden takes a shot. Clearance made by Neill Collins.71:35
Edward Upson produces a cross.70:08
Dave Kitson crosses the ball.68:33
Effort from deep inside the area by Jamie Murphy misses to the right of the goal.67:01
Neill Collins fouled by Paddy Madden, the ref awards a free kick. Free kick taken by Michael Doyle.66:41
Callum McFadzean takes a shot. Save made by Marek Stech.64:06
Dave Kitson produces a cross, Callum McFadzean takes a shot. Marek Stech makes a save.62:51
Joe Edwards has an effort at goal from outside the penalty area which goes wide right of the goal.62:42
Sam Foley crosses the ball, Matthew Hill makes a clearance.62:31
Sam Foley sends in a cross, blocked by Darryl Westlake.62:05
The ball is swung over by James Hayter, clearance made by Matthew Hill.59:56
Marek Stech takes the direct free kick.59:56 Booking
Booking Michael Doyle goes into the book.59:44
Foul by Michael Doyle on Joe Edwards, free kick awarded.57:54
Jamie Murphy takes a shot. Marek Stech makes a save.56:13
James Hayter is ruled offside. George Long takes the indirect free kick.54:11
Matthew Hill produces a cross, Dan Burn makes a clearance.51:40
Edward Upson takes a shot. Save made by George Long.51:17
Paddy Madden crosses the ball, Neill Collins makes a clearance.50:14
The ball is swung over by James Hayter, clearance by Jamie Murphy.48:05
James McAllister takes the inswinging corner, Kevin McDonald manages to make a clearance.47:56
The ball is sent over by Paddy Madden, blocked by Harry Maguire.45:52
Assist by Jamie Murphy.45:52 Goal scored
Goal! - Callum McFadzean - Sheff Utd 1 - 0 Yeovil Callum McFadzean finds the back of the net with a goal from deep inside the penalty box to the bottom left corner of the goal. Sheff Utd 1-0 Yeovil.45:48
Jamie Murphy produces a cross,45:01
The second half begins.45:00 +2:07 Half time
Half Time The ref blows to signal half-time.44:38
Free kick awarded for a foul by Edward Upson on Michael Doyle. Michael Doyle takes the direct free kick.42:04
The free kick is swung in right-footed by Darryl Westlake, free kick awarded for an unfair challenge on Byron Webster by Dave Kitson. Marek Stech takes the direct free kick.42:04 Booking
Booking Caution for James McAllister.41:45
James McAllister gives away a free kick for an unfair challenge on Callum McFadzean.41:32
The ball is swung over by Callum McFadzean, Byron Webster manages to make a clearance.41:12
Joe Edwards takes a shot. Darryl Westlake gets a block in.40:28
Kevin McDonald fouled by Joe Edwards, the ref awards a free kick. Direct free kick taken by Matthew Hill.38:26
Kevin Dawson concedes a free kick for a foul on Michael Doyle. Direct free kick taken by George Long.37:37
Direct free kick taken by James McAllister.37:37 Booking
Booking Dave Kitson receives a yellow card.37:25
Unfair challenge on James Hayter by Dave Kitson results in a free kick.36:26
Free kick awarded for an unfair challenge on Sam Foley by Dave Kitson. Direct free kick taken by Marek Stech.35:03
Kevin Dawson has an effort at goal from deep inside the area missing to the left of the target.34:53
The ball is crossed by Kevin Dawson.34:00
The referee blows for offside against Paddy Madden. Indirect free kick taken by George Long.32:40
The ball is sent over by Jamie Murphy, clearance made by Dan Burn.31:41
The ball is crossed by Michael Doyle, clearance by Luke Ayling.28:33
Indirect free kick taken by George Long.28:33 Substitution
Substitution Callum McFadzean on for Barry Robson.28:33
The assistant referee flags for offside against Paddy Madden.28:25
James Hayter produces a cross.25:06
The ball is sent over by Matthew Hill, James McAllister makes a clearance.23:43
Jamie Murphy fouled by Luke Ayling, the ref awards a free kick. Barry Robson delivers the ball, Effort on goal by Jamie Murphy from inside the penalty area goes harmlessly over the bar.23:09
The assistant referee flags for offside against Jamie Murphy. Marek Stech restarts play with the free kick.21:16
Unfair challenge on Dan Burn by Chris Porter results in a free kick. James McAllister restarts play with the free kick.18:16
Foul by Dan Burn on Chris Porter, free kick awarded. Darryl Westlake delivers the ball from the free kick right-footed from right wing, save made by Marek Stech.17:22
Unfair challenge on Sam Foley by Darryl Westlake results in a free kick. Direct free kick taken by James McAllister.15:47
James McAllister takes the inswinging corner, Unfair challenge on Harry Maguire by Dan Burn results in a free kick. George Long takes the free kick.15:40
Centre by James Hayter, blocked by Michael Doyle.14:59
The ball is crossed by Paddy Madden, Shot by Joe Edwards. Save by George Long.13:30
Foul by Kevin Dawson on Michael Doyle, free kick awarded. George Long takes the free kick.12:33
Barry Robson takes the outswinging corner, Headed effort from inside the area by Chris Porter misses to the left of the target.12:24
The ball is sent over by Matthew Hill, blocked by Luke Ayling.9:10
A cross is delivered by James McAllister.6:25
Unfair challenge on Barry Robson by Edward Upson results in a free kick. Barry Robson has a direct shot on goal from the free kick.4:41
Barry Robson crosses the ball, Header by Dave Kitson from deep inside the penalty area misses to the right of the target.3:13
Foul by Dave Kitson on Luke Ayling, free kick awarded. Free kick taken by Marek Stech.1:23
Centre by Dave Kitson.0:00
The game gets underway.
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