The Eagles reeled off five victories on the spin in the competition's inaugural 1992-1993 season, but that was not enough to keep them in the top flight.
Their winning streak this campaign, though, appears certain to result in the Selhurst Park outfit avoiding relegation from the Premier League for the first time in their five attempts.
The Welshman took charge in November with the Londoners joint bottom of the table, but they have since collected 33 points from 22 games to move to within touching distance of a top-half finish.
During this time period, Palace have accumulated more points than any side outside of the current top seven, and only six fewer than Arsenal and four fewer than reigning champions Manchester United.
A seven-point gap to the bottom three and a healthy goal difference means that Sam Allardyce's inconsistent side are unlikely to be dragged into trouble with four games of the season remaining.
George McCartney is pushing for a recall at the expense of Pablo Armero at left-back, while midfielder Kevin Nolan could also be fit to feature at Upton Park, with Mohamed Diame a candidate to make way.
Joey O'Brien, Marco Boriello and James Collins remain sidelined, but Andy Carroll is at last injury-free and will be hoping to use the final games of the campaign to press his England World Cup chances.
Palace will have a full squad to choose from if Yannick Bolasie and Kagisho Dikgacoi, who may be recalled to strengthen the midfield, recover from knocks. Thomas Ince is on standby if Pulis needs to make a change.
Jason Puncheon has scored four goals in his last three appearances for the visitors, who are unbeaten in their last five against West Ham in all competitions.
West Ham: LLWWLL
Possible starting lineups
West Ham: Adrian; Demel, Tomkins, Reid, McCartney; Noble, Nolan, Nocerino; Jarvis, Downing; Carroll
Palace: Speroni; Mariappa, Dann, Delaney, Ward; Jedinak, Dikgacoi, Ledley; Bolasie, Puncheon; Jerome
Sports Mole says: 1-1