Jack Collison came off the bench to score the winner deep into first-half injury time after being found by fellow substitute Ricardo Vaz Te.
The victory halted a run of five successive away league defeats and lifted the Hammers onto 33 points and further away from the drop zone.
Allardyce told Sky Sports: "It was the biggest one (victory in the season) without a doubt.
"I think we've played well enough the last few away games but not got any points and certainly the disappointment on Monday night having played so well against Tottenham and being in the lead and not getting anything out of that was a big pressure on us today and we've come up trumps."
Allardyce added it was a well deserved victory by his side, who limited Stoke to just a few chances.
He said: "It puts us back in the middle of the pack in the middle of the table again.
"(We are on) 33 points, ever closer to that big 40 that we all look for, but especially the first year (back) in (the Premier League)."
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