Luongo set up Nathan Byrne for the winner in stoppage time as Swindon came from behind to take a narrow advantage in the tie.
Swindon manager Mark Cooper said he was proud of his players, who had given the Robins a chance of making up for three previous play-off defeats in 2004, 2010 and 2013.
"For 20 minutes we really struggled to get to grips with Sheffield United's intensity," Cooper said.
"They came out really strong and pressed and the crowd got behind them and we struggled to cope.
"But after that I thought we were outstanding. We played some brilliant football in a real pressure-cooker atmosphere and I'm really proud of the players."
This means that Cooper's side go into the second leg only needing a draw to book a place at Wembley in the play-off final.
The Lilywhites started well after Jermaine Beckford found the back of the net after just six minutes at the Proact Stadium. Chesterfield responded well and dominated most of the match, but were unable to find their way past a solid Preston defence lead by promising Australian defender Wright.
Former Socceroos midfielder Neil Kilkenny also featured in the match, coming off the bench to make a 30-minute cameo for Preston.
The second leg between Preston and Chesterfield will take place on Sunday, with the winner facing either Swindon or Sheffield in the final at Wembley after their return bout on Monday night.