Just three days after succeeding Paul Ince as Rovers manager, Allardyce took charge of his first match and inspired a remarkable upturn in Blackburn's fortunes.
South African forward Benni McCarthy's double and a Jason Roberts strike within the first 27 minutes at Ewood Park clinched Rovers' first win in 12 matches and ended a six-match losing run that had forced Blackburn to sack Ince earlier this week.
Blackburn remain in the relegation zone but Allardyce has already provided hope where none existed under Ince.
Allardyce handed David Dunn his first start since August as the new boss made three changes to the team thrashed at Wigan in Ince's final match.
Roque Santa Cruz was absent after injuring a calf in training, with McCarthy coming in for his 100th Rovers appearance alongside Roberts in the forward line.
Stoke suffered a blow when Danish keeper Thomas Sorensen was injured in the warm-up and replaced by Steve Simonsen.
That was a clear sign it was going to Allardyce's day. He received a warm welcome from the fans when he came onto the pitch before kick-off with a Rovers scarf around his shoulders.
Allardyce had to watch Rovers survive an early barrage from Stoke, with Glenn Whelan's cross-shot almost catching out Paul Robinson.
But it wasn't long before he was out of his seat celebrating a goal against the run of play in the ninth minute.
McCarthy played a neat ball into the penalty area for Morten Gamst Pedersen and he was crudely hacked down by Ibrahima Sonko.
Referee Peter Walton pointed to the spot and McCarthy blasted home his fifth goal of the season.
If that was a fairytale beginning for Allardyce, there was even better to come in the 18th minute.
McCarthy laid off Andre Ooijer's throw to Brett Emerton and his drilled cross to the far post was deflected back into the path of Roberts, who drove home from close range.
Allardyce's last match as a manager had been a dour FA Cup goalless draw against Stoke at the end of his brief Newcastle reign. This was far more to his liking.
Stoke have been unable to repeat their impressive home form on their travels and the match was effectively over when they conceded again in the 27th minute.
Roberts and McCarthy were playing with a potent combination of pace and power that left Stoke in tatters.
McCarthy back-heeled the ball to Roberts and Simonsen could only parry his shot. The ball ran kindly for McCarthy and he calmly slotted home.
Stoke boss Tony Pulis sent on Tom Soares and Michael Tonge for Rory Delap and Vincent Pericard in an attempt to spark his side into life in the second half. But it was Blackburn who came close to increasing their lead when Dunn's delivery almost picked out McCarthy before the defence scrambled clear.
Stoke enjoyed most of the possession after the interval but only threatened when Robinson dived low to his left to save Ricardo Fuller's glancing header from a Danny Higginbotham cross.
Simonsen pulled off a great save from Pedersen's close-range strike and Roberts should have doubled his tally for the day seconds later but the keeper deflected his shot wide.
From the resulting corner McCarthy's glanced off the post, but it didn't matter. Allardyce had already made more than enough of an impact already.