United's play-off hoodoo continues as Yeovil clawed a one-goal first leg deficit to win in Somerset on Bank Holiday Monday.
Kevin Dawson cancelled out Callum McFadzean's first leg goal and Ed Upson scored what proved to be the winner late on at Huish Park.
Jamie Murphy hit the crossbar for the Blades but the season came to an untimely end as Yeovil booked their Wembley place.
Teenagers McFadzean and Ironside were handed starts in the second leg. Goalscorer in the first leg, McFadzean, took the place of the injured Robson, whilst Ironside replaced Kitson, who dropped to the bench and was joined by the fit-again Flynn. Home boss Johnson named the same team that started the Bramall Lane encounter.
McFadzean began on the right flank and Ironside partnered Porter in attack but Yeovil were the first to show and Burn headed a McAllister corner wide inside the first two minutes. With Huish Park particularly vociferous, the home side were buoyed and took just six minutes to level the tie on aggregate - Edwards threaded a pass through the defence to meet the run of DAWSON, who calmly slotted under Long in front of the Unitedites in the open way end.
Three long-range shots from McDonald failed to trouble Stech in the opening 15 minutes, although the Yeovil goalkeeper was required to tip over a Doyle effort after a break out of defence. McFadzean and Ironside also had shots blocked as the Blades looked to respond to the early setback.
Despite the May Day sunshine, the early action was frantic and the home side came close to doubling their tally on 22 minutes following another accurate pass but this time Long saved with his legs to prevent Edwards scoring. Similarly, Stech saved with his pins to stop Murphy moments later after both Ironside and Porter caused problems for the Yeovil defence.
Murphy went closer still on 34 minutes, his curler beating Stech but connecting with the crossbar after an enterprising run from McFadzean and then Ironside was called offside as he met a right-wing cross.
Maguire was the first in the book, guilty of fouling Madden on the edge of the box, and the resulting free-kick from McAllister deflected off the wall for a corner, but the Blades were on top as half-time approached. Another effort from Murphy deflected off Burn for a corner, which Porter looped onto the roof of the net after a spell of head tennis.
Kicking towards the Blades fans in the second period, the visitors almost made the best possible start but Porter's initial effort was blocked by Burn and the rebound from the number nine only found the side-netting.
Yeovil also had two great chances early in the half but their leading scorer, Madden, could not add to his tally. Firstly, he got the better of Westlake but failed to get a good connection with his shot and Long saved comfortably, whilst the second, on 53 minutes, saw him creep in at the back post but he failed to find the target from Ayling's cross.
The first substitution of the game came from Morgan, Higginbotham replacing Westlake with Hill switching to right-back, followed by Kitson taking over from Ironside just after the hour mark.
In the sapping conditions, the frantic end-to-end action continued with both sides creating half-chances as the game approached the last 20 minutes of regulation time. Maguire headed wide a Murphy cross after Porter had earned a corner, whilst Murphy also drilled across goal moments later.
As the watch ticked around to 80 minutes, Hayter connected with a Foley cross but failed to find the target from six yards, but the sucker punch was moments away. With just over 84 minutes gone, Ayling's cross from the right saw UPSON sneak in unmarked to head past the over exposed Long.
Flynn was introduced as United chased the game in the closing minutes. Doyle almost put Porter through, but Foley almost added a third after the Blades failed to clear in the left-back area.
Collins was added to the forward line and Porter almost got on the end of a Murphy cross as four minutes of added time was announced. McDonald was booked for dissent but the Blades were unable to trouble Stech once again and it was the home side who celebrated at referee Gibbs' final whistle.
Yeovil: Stech, Ayling, McAllister, Webster, Upton, Hayter (Hinds 90), Foley, Madden, Burn, Edwards, Dawson.
Unused: Blizzard, Williams, Stewart, Maksimenko, Young, Balanta.
Blades: Long, Westlake (Higginbotham 55), Maguire, Hill, Doyle, Porter, McDonald, Collins, Murphy, Ironside (Kitson 64), McFadzean (Flynn 87).
Unused: Chapell, Whitehouse, Barry, Coyne.