Frankie McAvoy's men were behind inside 10 minutes in Yorkshire, Morgan Gibbs-White putting the Blades ahead.
They responded before the break through Daniel Johnson, who collected a wonderful ball from Ryan Ledson expertly, rounding the 'keeper and slotting into an empty net.
United thought they had won it when Sander Berge scored with just six minutes to go but Riis had other ideas to spark pandemonium in the away end behind the goal he scored in.
The Dane had the chance to put his side in the lead at 1-1, just before the home side took the lead. On the balance of things, the 23-year-old felt his side deserved at least their share of the spoils but is not getting too carried away despite the jubilation.
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"We definitely deserved the point, if not all three," he said.
"In the first half we had the most chances, I know they had chances too but we played really well.
"In the second half they were on top a bit but we had chances to get even more goals.
"The chance I had at 1-1, I need to put that away.
"When they score straight away you get really disappointed and they look like they're going to take all three points.
"To score in the last minute, it feels like a win but we've got to remember that it's still only one point.
"We did really well, we need to keep playing like this - I'm really pleased."
Having just seen a huge chance saved, it came to Riis to right his wrong. The Lilywhites' top scorer admits he felt the nerves as the ball landed at his feet following fine work from Jordan Storey to keep the ball alive.
His goal triggered joyous scenes, with goalkeeper Daniel Iversen even running the length of the pitch to join in - as did a couple of PNE fans that got a taste of the Bramall Lane pitch.
"It was a bit of everything," Riis explained.
"I was really nervous when I took that first touch because I knew there were a lot of bodies on the line so I just tried to smash it in the bottom of the net.
"I was just so happy to see it go in.
"It's always amazing to score in front of the fans, they were great again today.
"I'm really pleased to show them that I can score again.
"I'm really happy to help the team with goals. I'm pleased to have six, but it should have been seven!"
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