On six minutes, Yeovil's Paddy Madden made it 1–0 with a shot from the edge of the Brentford penalty area with the outside of his right boot into the top-right corner of Simon Moore's goal.
Despite pressure from Brentford with Moore saving attempts from Clayton Donaldson, Adam Forshaw and Bradley Wright-Phillips, the score remained 2–1 and Yeovil were promoted to the Championship.
The first half ended goalless with the best chance falling to Barry Robson; his free kick went just wide of the Yeovil goalpost.
Callum McFadzean came on after half-time to replace Robson and within a minute of the second half, his shot deflected past Marek Štěch in the Yeovil goal to give Sheffield United the advantage.
Kevin Dawson levelled the tie on aggregate when he put the home side ahead on five minutes after a pass from Ed Upson.
After a goalless first half, Swindon's Massimo Luongo opened the scoring in the 70th minute with a curling shot from the edge of the penalty area.
The home side dominated the early play and went ahead midway through the half after Adam Rooney steered the ball into his own net from a corner.
Joe Devera's 57th-minute volley made it 3–2 and in injury time Aden Flint's headed goal levelled the match at 3–3, and the aggregate score at 4–4.
Despite Swindon's Nathan Byrne being sent off after receiving a second yellow card for handball, the extra-time period ended goalless and the game went to a penalty shootout.
[17][18] The remainder of the first half saw few chances, but in the 42nd minute, a corner from Sam Foley to the far post found Dan Burn who headed the ball into the six-yard box.
[18] In injury time, Jake Bidwell's cross was headed goalwards by Marcello Trotta but it was caught by Štěch in the Yeovil goal.
[17] Neither side made any changes to their personnel during half-time and in the opening moments of the second half, Brentford went on the attack with an off-target shot from Donaldson.
[18] Assistant referees: Derek Eaton[19] Alan Young[19] Fourth official: Graham Scott[19] Reserve Assistant Referee: John Hopkins[19] Match rules: The Yeovil manager Gary Johnson described Madden's opening goal as "a sublime piece of ingenuity".