That same route to goal almost provided Palace with their second 20 minutes later, Blanchard sprinting down the right and cutting the ball back towards Olding, but the midfielder's effort was blocked.
As the game ticked into six minutes of injury time, Blanchard enjoyed a further opportunity to shoot and did so powerfully from inside the area, but cleared the crossbar with her attempt.
The hosts poured bodies forwards in the remaining minutes of the game, but Palace remained resolute in their defending, and there were no further chances as the south London side returned home content with another three points.
The result sees Palace stay sixth in the Women's Championship, but now within just three points of third place.
After a great result this week, the Eagles will hope to keep up their strong recent form in their next match against Birmingham City on Wednesday 22nd March.
Sheffield United: Stenson (GK), Newsham, Barker, Hartley, Riglar, Sweetman-Kirk (Clarke, 73), Rayner, Paul, Lord-Mears (Cusack, 45), Enderby, Wilcock (Walters, 45)<br>
Subs not used: Brown, Graham, Davies, Haywood, Muir, Francis-Jones
Palace: Kitching (GK), Reilly, Waldie, Doran, Hughes (Bailey-Gayle, 84) ,Filbey, Blanchard, Olding, Everett, Haines (Guyatt, 90+1), Sharpe<br>
Subs not used: Negri (GK), Johnson, Gibbons, Arthur, Wilson-White