Matheus Pereira and Callum Robinson both netted braces while Mbaye Diagne was also on target as the Baggies smashed Thomas Tuchel's side 5-2.
The hosts took the lead just before the half-hour mark through Christian Pulisic and then saw Thiago Silva sent off just moments later.
But that should take nothing away from Albion's outstanding display with the Baggies scoring five outstanding goals to deservedly win the game.
The result means, with eight matches left to play, Allardyce's men sit seven points from safety with the Baggies next in action against Southampton a week on Monday.
"The quality of the performance and the way we demolished Chelsea, perhaps it gives us a little more than hope," Allardyce said.
"Can we now reach this level of performance again, starting against Southampton a week on Monday?
"It keeps us going, it keeps us alive.
"We’d have liked it (the result) to have come quicker but we can’t complain about the quality of this performance and the outstanding performance of all the players.
"That is what the Premier League is about - teams at the bottom can beat anybody, they can beat the teams at the top when they perform at their best and we performed at our best.
"People cannot say that Chelsea were under par or it's because they went down to 10 men.
"They must say, everybody must say, it was because of the quality of West Brom's performance today."
Speaking after the defeat to Crystal Palace last time out, Allardyce said his time needed to win six of their remaining last nine matches to have a chance of staying up.
"I said we needed to win six out of the last nine, now we need five out of the last eight," he added.
"Still that might not be enough but let’s start with Southampton and let’s try and see if we can get another fantastic victory there."