Shortly after the hour mark, Palace deservedly found the breakthrough. Olding scored her first goal of the season in emphatic style as her excellent long-range strike whistled into the bottom corner to put the Eagles in front.
Davenport's side were beginning to find their attacking rhythm, as Haines picked out Annabel Blanchard in the 68th minute with another perfect long ball, but the winger fired wide of the post.
After a flurry of chances, Sheffield United produced an equaliser in the 75th minute, with Bex Rayner's powerful volley from the edge of the box cannoning in off the bar.
With the scores level, the away side seemed to have found some confidence, with Sweetman-Kirk's strike from outside the area narrowly gliding over the bar three minutes later.
This confidence was short lived though, as a well-worked counter-attack found Haines in the box, who neatly placed her finish into the top corner – restoring Palace's advantage in the 80th minute.
The Eagles were under pressure straight after the restart as Sheffield United saw a number of efforts kept out in quick succession, the latter of which looped over Kitching, whose quick reactions prevented the ball from finding the net.
Despite eight minutes of added-time due to a number of injuries, Palace defended resiliently to shut out any further attacks and secure all three points.
Back-to-back home wins sees Davenport’s side stay in sixth place in the Women's Championship, now just five points off third place. They return to Hayes Lane next Sunday, 5th March to face title-chasing Bristol City.
Palace: Kitching (GK), Reilly (Johnson, 45), Everett (Arthur, 15), Waldie, Reilly, Filbey, Doran, Olding (Bailey-Gayle, 90), Haines, Blanchard, Dean, Sharpe
Subs not used: Negri (GK), Hughes, Gibbons
Sheffield United: Stenson (GK), Newsham, Barker (Cusack, 72), Hartley, Riglar, Sweetman-Kirk, Rayner, Paul, Lord-Mears (Muir, 72), Enderby (Walters, 30), Haywood (Wilcock, 64)
Subs not used: Davies (GK), Francis-Jones, Brown, Graham