The victory kept the Hammers in the top four of the table, and there is a growing belief around Upton Park that they could gatecrash what has been an exclusive European party this season.
Diafra Sakho continued his record of scoring in every West Ham game in which he has started by notching for the seventh match in a row, but he is a major doubt for their trip to the Potteries after injuring his shoulder against City.
His potential absence is cushioned by the fact that fellow summer signings Enner Valencia and Morgan Amalfitano are also chipping in with goals, but it is the capture of Alex Song which could prove to be Allardyce's shrewdest piece of business since his Bolton Wanderers days.
The Cameroonian midfielder has been instrumental in West Ham's success since joining on loan from Barcelona and has immediately formed an effective partnership with Mark Noble which will keep fit-again Cheikhou Kouyate on the bench.
Club-record signing Andy Carroll, who is yet to feature this season because of an ankle injury, is nearing a return, but this weekend perhaps comes too soon for him and therefore Carlton Cole is on standby to deputise for Sakho in attack.
With Mauro Zarate and Guy Demel still nursing knocks, Allardyce's only other selection decision seems to be whether to retain James Collins at centre-back, or recall James Tomkins now that the academy graduate has recovered from the injury that has cost him two matches.
Their latest defeat came in the Capital One Cup fourth round to Southampton on Wednesday, as they came from two goals down to level the match before conceding late on after the dismissal of Peter Crouch.
Crouch joins Phil Bardsley in being suspended for the visit of the Irons, so Hughes will be forced into a reshuffle, with Geoff Cameron switching from midfield to right-back and Mame Biram Diouf playing centrally up top.
West Ham: WWWLWD
Possible starting lineups
Stoke: Begovic; Cameron, Wilson, Shawcross, Pieters; N'Zonzi, Sidwell; Walters, Adam, Moses; Diouf
West Ham: Adrian; Jenkinson, Collins, Reid, Cresswell; Song, Noble, Amalfitano, Downing; Cole, Valencia
Sports Mole says: 0-1