The Tigers held league leaders Chelsea 1-1 last Tuesday then beat Manchester City 2-1 on Saturday to claim their first win in 12.
Those crucial four points have propelled Hull out of the drop zone up to 14th place as manager Phil Brown prepares to renew acquaintances with Allardyce, to whom he was assistant boss at Bolton.
"Those results are what makes the Premier League so exciting because they aren't what should happen," Allardyce told Sky Sports News.
"Full marks to my old mate there, Phil Brown, and to his staff and players for coming through a difficult period and coming out with some terrific results.
"We're all very pleased when we win matches but when we get them off the big boys it's a massive bonus.
"It boosts the confidence of the players beyond the norm and I think that's why we're going to have such a difficult game on Wednesday night.
"I watched them against Chelsea and I've seen the highlights of the game against Manchester City," he added.
"They're in top form at the moment with those two results so they'll be coming here very confident and feeling very capable of getting a result against us."
Rovers boosted their own survival hopes with a run of seven points from a possible nine last month.
They then suffered a 3-0 defeat at Stoke on Saturday to leave them in 12th place, four points ahead of Hull, but Allardyce is hoping they can put that setback behind them at the first attempt.
"Stoke were a lot better than we were, which was a surprise to me based on the form that we showed against Fulham, Wigan and particularly West Ham," added the Blackburn boss.
"But it's gone now and hopefully it will kick-start us into a good performance on Wednesday night against Hull City, which is a game that will not be as easy as some of the Blackburn fans might think."
Source: Team Talk
Source: Team Talk