Despite recent difficulties in the league, Palace were hoping to build on an impressive performance in the FA Cup third round, where they scored five goals against Watford.
Defender Lizzie Waldie, midfielder Kirsten Reilly and forward Paige Bailey-Gayle were reintroduced to the starting XI by manager Dean Davenport, following a disappointing 3-2 loss to Coventry United last time out.
As the match kicked-off, both teams struggled to keep possession of the ball amidst overcast conditions, but Durham were first to go close through Mollie Lambert, whose break down the left flank ended in a shot across goal which forced Fran Kitching into an early save.
The reacting Palace defenders could only half-clear and the ball dropped kindly for Hepple on the edge of the box. The Durham attacker bent an effort onto the roof of the crossbar, the rebound bouncing kindly for Kitching to dive on.
It was only a temporary reprieve. A chipped ball forwards found Rio Hardy running in behind the Palace defence at full speed, and inching into the box, she squared for Lambert to tap home from the centre of the box to give Durham an early lead.
Once the hosts scored their first goal, they were seemingly on a roll, as six minutes later they scored another.
After a long free-kick forwards from Durham ‘keeper Nadisha McAloon was poked over the backline, Jessica Clarke spotted an opening near the right side of the box and volleyed across goal to score her side’s second. The finish was excellent, but Palace will have felt it could have been avoided defensively.
Just before half-time, Durham continued to pile the pressure on Palace from set-pieces, but the Eagles did well to throw bodies in the way of Sarah Robson’s close-range header and deflect it over the bar.
With their Cup hopes on the brink, Palace came out for the second half with a renewed sense of purpose – but it was the hosts who created the next opportunity as Hardy was denied by Kitching, who stood tall and reacted quickly to block the striker’s volleyed finish.
As the Eagles pushed players forwards, space opened up for Hepple to sprint into, but she twice struck efforts wide when the Durham winger perhaps had more time and space than she had imagined.
Palace did manage to mount several concerted spells of pressure, but Durham’s defence proved too strong to create many meaningful opportunities.
Yet their spirit remained strong and, after Bridget Galloway beat Kitching to a long ball over the top, Lambert looked set to convert the rebound for Durham’s third – only for Annabel Johnson to produce an outstanding last-ditch challenge to prevent the goal.
As the seconds ticked down, Polly Doran created her side’s best chance of the match, squaring smartly for Bailey-Gayle – but the winger’s placed effort flew wide past the goal.
Seven minutes of injury time was signalled – but three minutes into the additional period, Palace’s Cup exit was confirmed. Lauren Briggs booted the ball powerfully across the penalty area where it found Lily Crosthwaite, who finished crisply from close range to seal Durham’s 3-0 win.
Palace will hope to turn their recent form around when they travel to Southampton – and St Mary’s Stadium – in the Women’s Championship next weekend. Kick-off is at 14:00 GMT on Sunday, 5th February.
Palace: Kitching (GK), Johnson, Waldie, Reilly, Doran, Filbey, Arthur (Olding, 45), Gibbons, Haines (Blanchard, 45), Bailey-Gayle, Hughes
Subs not used: Everett, Peplow, Sharpe, Dean, Negri, Guyatt