Wijnaldum scored the only goal as Liverpool continued their perfect start to the Premier League season with victory at a raucous Bramall Lane.
But the winner was a moment to forget for otherwise faultless Blades goalkeeper Dean Henderson, who spilled the Dutchman's tame effort before it squirmed agonisingly over the line.
It meant relief for Jurgen Klopp's side, who were far from their best in South Yorkshire - and left thankful that the hosts could not find a way through in a game where they matched the European champions in many respects.
Substitute Leon Clarke should have levelled it late on, but blazed over.
Wijnaldum said at the final whistle: "We didn't start the game well. In the first half we slowed the game down too much and that's why they could stop us.
"It was not the best game we had but we won. A few years ago we would not have been able to win these games.
"It could be a really important three points. It's really good to keep collecting the points."