Kieron Freeman’s first-half strike had given the hosts the lead at the interval before Sam Ricketts’ brilliant header after the break left the tie between the league’s fourth and fifth-place sides delicately poised ahead of Monday’s second leg at The County Ground.
Blades ‘keeper Mark Howard denied Ben Gladwin from the penalty spot in the first half but, with the game destined for stalement, Byrne’s 25-yard strike evaded his clutches as the Robins claimed their first win at Bramall Lane since 1970.
Sheffield United shrugged off their label of slow starters and flew out of the blocks in front a home crowd desperate to end their dismal run of seven unsuccessful play-off campaigns.
The hosts’ bright start was almost rewarded with a penalty ten minutes in when Jamie Murphy’s cross was handled by Robins skipper Nathan Thompson in the area, but referee Darren Bond was unmoved.
The Blades were not to be denied, though, as Freeman’s first-time strike from Ryan Flynn’s cross beat Swindon ‘keeper Wes Foderingham at his near post after 19 minutes to give the host a deserved lead.
The referee was centre-stage just before the half-hour when he showed no hesitation in pointing to the spot after Byrne was tripped in the area by Bob Harris.
Gladwin stepped up but saw his poor spot-kick palmed away from goal by Howard as the Blades weathered a late rally from the visitors to go in in front at the break.
The tide clearly turned in favour of Swindon after the break as Mark Cooper’s side pushed for the equaliser.
Michael Smith saw a glorious chance elude both he and his side as Jordan Turnbull’s cross from the left floated over the striker’s head as just he stooped to head home on 47 minutes.
Life-long Swindon fan Ricketts took matters into his own hands, hauling his boyhood club level on 51 minutes with a wonderful header from Byrne’s corner.
Both sides exchanged blows from then on as Ricketts and Flynn came close to handing their sides the advantage.
The introduction of Matt Done reignited the hosts who mounted a late push for that all important winner, but Steven Davies’ inexcusable missed header from three yards appeared to have ensureD the game would end level.
A late flurry of corners for United allowed Swindon to break in the closing stages where Byrne’s long-range effort skipped over Howard’s dive to hand to the Robin’s 45-year wait for a victory in the Steel City, and hand them the advantage in the race for Wembley.
Man of the Match: Yaser Kasim