The Danish striker grabbed his sixth goal of the season in all competitions after home substitute Sander Berge thought his 84th-minute effort had secured the spoils for the hosts, who had earlier seen Morgan Gibbs-White's opener cancelled out by Daniel Johnson's 50th league goal.
Gibbs-White claimed his second goal in as many outings following a loan move from Wolves after a weak clearance by Patrick Bauer was picked up on the left wing by Luke Freeman.
After Freeman's cross was then contested in the air by Bauer and Iliman Ndiaye, a sliding Gibbs-White beat Daniel Iversen from close to the penalty spot on seven minutes.
Preston, however, were back on terms in the 19th minute when Ryan Ledson's long ball from deep in his own half was taken on his chest expertly by Johnson.
That immaculate piece of skill took him past Swedish international keeper Robin Olsen who, on his debut for the hosts, had raced to the edge of his box and was only able to look back over his shoulder as the Lilywhites playmaker completed the formality of finding an unguarded net.
United responded positively as Oliver Norwood went close with a fierce 20-yard drive that whistled just over and Freeman might have gone on to regain the lead for Slavisa Jokanovic's men going into the interval, but he sidefooted over from 12 yards after George Baldock had raced on to Norwood's ball down the right flank.
After the break, Bauer took the sting out of a Billy Sharp strike that looped into the arms of Iversen and the veteran home striker also delivered a cross that Ndiaye headed past the near post.
For the visitors, Riis turned Jack Robinson far too easily through the right channel but then drove wide before Gibbs-White lifted a 25-yard free-kick over at the other end.
As play began to swing from end to end, away substitute Brad Potts could not guide his header on target from an inswinging Ledson free-kick and then John Fleck showed excellent determination to charge clear on goal, but Iversen was equal to his attempt to deftly lift the ball over him.
Next, Rhian Brewster's 20-yard shot was gathered by Iversen before Olsen charged out of his goal to deny Riis with his feet.
Norway international Berge was not to be denied, though, when he sidefooted between Iversen's legs from eight yards after Sharp's shot had been blocked following another forward surge by Fleck.
But one final opportunity saw Ledson pump a free-kick into the home box that skimmed off Robinson's head and Jordan Storey then lofted a cross to the far post from close to the right byline and Riis kept his cool to fire in from eight yards.