The Danish striker scored PNE's 89th minute equaliser in last night's 2-2 draw with the Blades at Deepdale.
They fought back from being 2-0 down before half-time and did it with 10 men after Andrew Hughes had been sent-off.
Alan Browne started the ball rolling on the comeback in the 71st minute, firing home a cross from Daniel Johnson.
Then with the game in the final minutes of regulation time, Ched Evans' superb low ball across the box allowed Riis to slide in and score at the far post.
Riis had scored a stoppage-time leveller for North End against United in the reverse fixture at Bramall Lane in September - that game also finished 2-2.
Last night's was his first goal in eight games, the 23-year-old last scoring in the 2-1 win at Middlesbrough in November.
Riis said: "I tried to stay on the back of the defender so he couldn't see me. I was thinking Ched was going to cut it back but he couldn't really get around it.
"So I ran off the back off the defender and luckily it went in. It hit the post so for a moment I was nervous.
"It was nice to score with all the fans there and playing at night here is enjoyable.
"We had the ball less than we normally do because of the red card but I thought we still did well."
Turning to the topic of scoring twice in similar circumstances against the Blades, Riis was happy to have done so.
He said: "I have scored two in two now against Sheffield United. We only got two points out of the two games and obviously we would have liked to get more.
"But we'll take a point from this one with where we were in the game earlier.
"I think our second-half performance deserved a point, I didn't think Sheffield United played that well in the second half and we dug in.
"We all worked hard and that got us to the point where we were still in the game at the end and scored the equaliser.
"As a team we believed in ourselves and stayed in the game.
"At half-time I thought it was going to be a long night ahead of us. We were thinking we didn't want to get beat three or four nil,
"The aim was to get a goal back and go from there. That is what we did, that is why we had the chance in the end.
"It felt like a win so we can progress to Swansea on Saturday with a lot of confidence."
Hughes' dismissal came for a foul on Rhian Brewster, referee David Webb pointing to the penalty spot and then reaching for his pocket for the red card.
Billy Sharp scored the penalty, adding to the lead which Jayden Bogle had given the visitors in the 17th minute.
A red card for denying an opponent a goalscoring opportunity carries a one-match suspension which will rule Hughes out of the visit to Swansea.
North End can appeal if they so wish with it being a straight red card.
Meanwhile, PNE defender Jordan Storey is set to join Sheffield Wednesday on loan today for the rest of the season.
Reports in Yorkshire suggested he was with the Owls last night finalising the switch.
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