The manner of the win, with the home side clawing back from the shock of conceding a third minute opener to Gabriel Agbonlahor, convinced Allardyce his side has what it takes to climb the table.
"We've burst all the odds today and it shows the determination of our squad and the quality of our team," said a visibly delighted Allardyce. "Now what we have to do is hit those consistent performances.
"I'm delighted with the way we kicked on after going a goal down in the first few minutes. It really only knocked us back for a few minutes. We came storming back and we got what we deserved."
Agbonlahor's fourth league goal of the season, a simple rolled finish past Paul Robinson with plenty of space in the box, looked likely to help buoyant Villa maintain their 100% away league start.
Arriving at Ewood Park on the back of four straight wins after their opening day defeat at Wigan, Villa started with a swagger which looked set to leave Rovers looking clumsy and short on class.
Ultimately, however, Agbonlahor's continued form was to prove a solitary bright spot for a plainly dejected Villa boss Martin O'Neill.
He said: "He's been brilliant for us. But we were hoping to get something out of today."
After John Carew had missed an Ashley Young cross by inches in front of goal, that class was underlined by the unlikely figure of Rovers central defender Christopher Samba, who swept home well after a nod-down by Franco Di Santo.
Samba's form at the back is a plus for Allardyce, who admitted: "His finish was excellent and he showed the forwards how to do it. Benni McCarthy couldn't have done it any better and he's our best goalscorer.
"In many ways I think Chris Samba was our saviour last season playing up front. He creates such a presence up there.
"But at the back we've limited a very, very talented Aston Villa front line to very few chances, which is very pleasing indeed."
In a lively end-to-end clash, Young flashed a shot across the face of goal before Friedel pulled off a stunning point-blank save to tip an overhead from Dunn over the bar.
With Dunn increasingly influential, Rovers began the second half in fine form, with Di Santo squirming a header wide before their impetus threatened to wane when Grella was dismissed for a clumsy challenge on James Milner.
Allardyce had no complaints about the sending-off nor the reaction of his side, who poured forward and had chances through Brett Emerton and Di Santo before Richard Dunne's handball presented Dunn with his spot-kick chance.
O'Neill, who had issues with the awarding of the penalty, added: "We tried to get a little bit of extra width in the side to try to break through but the sending-off may well have galvanised Blackburn.
"Perhaps we didn't create as many clear-cut chances in the second half as we might have done, but I felt we were worthy of a point.
"We were never out of the game and I'm naturally disappointed to have conceded so late on."