For two teams locked in a relegation battle, the hunger to claim three points was evident in a thrilling first half from which the first four shots on target all led to goals.
The opener fell the way of the visitors, who after netting the latest-ever PL goal nine days ago, scored here within 21 seconds.
A nine-pass move was put away by Ben Brereton Díaz - a trademark curler from the edge of the area into the bottom-right corner to make it two strikes in as many appearances for his new loan club.
All a deflated Selhurst Park could do was watch on - ‘wasted potential on and off the pitch’ was the message sent from the stands after their heavy defeat to Arsenal.
To restore some hope, Eberechi Eze produced an acrobatic flick on the end of Olise’s cross to pull his side level out of nowhere, though again all it took was three minutes for the Blades to retake their advantage.
Countering with speed, Oliver McBurnie held off two challenges before laying the ball to James McAtee.
The Manchester City loanee fired his shot off early, and to his fortune, it looped over Dean Henderson via a deflection off Marc Guéhi.
Finally, the last act of the half saw Olise and Eze combine once more, with one quick pass from Frenchman to Englishman helping the latter open up the space to curl a stunning strike beyond Ivo Grbić from distance, doubling his goals for the day.
From that perspective too, the hosts’ attacking troubles had been well and truly eased by the return of Olise from injury, as they had failed to score in the three fixtures he sat out.
A blockbuster second half was teed up to decide the winner.
Perhaps falling behind twice was a good omen in disguise for Palace given the fact they had failed to win the two most recent matches they led at home, and it was Olise who confirmed that as he added what turned out to be the winner 23 minutes before FT.
Jean-Philippe Mateta’s blocked cross fell the way of his teammate, who took the half-volley on from outside the box and watched it nestle in the bottom-left corner.
That was the winger’s final act as he exited with another injury - not something the home support wanted to witness after a man-of-the-match display, though at least in the short-term it extends the gap between their team and the bottom three to six points.
Meanwhile, Sheffield United remain rooted to the foot of the table, now nine points from safety.
Flashscore Man of the Match: Michael Olise (Crystal Palace)
