Liddell struck twice in the space of a minute after Danny Cullip had equalised for the Blades following Gareth Barry's opener just after half-time.
The Blades played the better football and only Thomas Sorensen prevented them from going in ahead at the interval.
But it was the Villa keeper's misjudgement that handed the Championship side the decisive third goal which saw Villa go out in the third round for the fourth consecutive season.
Villa came to the game on a dreadful run of form in the Premiership which had seen them fail to secure a point since the 1-1 draw with Liverpool at the start of December.
Warnock's side, however, boasted a record of just one defeat in 11 which had seen them consolidate a play-off place in the Championship.
The teams were greeted by a hailstorm and swirling wind which made the prospect of flowing football unlikely.
United went straight on the attack and in the sixth minute Jon Harley swung in a curling cross which Bromby could not get on target after he stole in at the far post.
However, the Blades had settled quickly with Derek Geary and Alan Quinn linking up well.
Barry hit a 25-yard shot over the top for Villa before Phil Jagielka volleyed narrowly wide after Quinn laid the ball off following a first-time pass hit fiercely across the area by Harley.
Villa boss David O'Leary had to restrain assistant Roy Aitken after he appeared to have words with Warnock.
Wright almost scored an own goal with a curling clearance after the ball ricocheted in the six-yard box following a Barry corner.
Jagielka's looping header following intricate play by Bromby and Andy Liddell was tipped over by Sorensen and it was United who were looking the likelier to score.
Gray missed a glorious chance after Liddell played him in with a backheel but he played it too close to Sorensen.
Sorensen then pulled off a fantastic save following another Jagielka header from Liddell's corner which was pushed away by the keeper as the Blades cranked up the pressure.
Then Liddell had a long-range shot saved from the resulting corner before Quinn had a 20-yard drive saved after being played in by Michael Tonge following a teasing run by the youngster.
Nick Montgomery came on for the Blades to replace Derek Geary who had been injured in a challenge with Delaney, while O'Leary decided to keep things as they were after the break.
His half-time team talk must have been effective as Villa took a surprise lead through Barry in the 47th minute to score the club's first goal since the defeat by Birmingham last month.
The midfielder was played in by Hendrie whose ball split the defence and he hit a half-volley from 22 yards which looped over stranded Blades keeper Paddy Kenny and nestled into the net.
United were shaken but they were on level terms in the 55th minute when Harley's inswinging corner evaded Delaney and Cole and was poked in from three yards out by Cullip for his first goal for the club.
Villa had an appeal for a penalty turned down but it would have been harsh with Barry's shot hit straight at Wright's hand without any time for the defender to react.
Cole's afternoon ended early when he was replaced by FA Cup debutant Luke Moore with the on-loan Chelsea striker still searching for his first goal for Villa since August 28th.
The Blades then took the lead in controverisal circumstances when Liddell was judged to have been onside from Quinn's flick-on and he drove the ball fiercely through Sorensen's legs before the same player gave them a two-goal cushion with just seven minutes to go with his second goal in a minute.
Tonge made good ground before passing to Liddell on the right of the area and his fierce first-time shot, which took a slight deflection off Jlloyd Samuel, caught Sorensen unawares and the ball squirmed under his body and into the net.
The keeper made a good save from Tonge just before the end but the damage had already been done as the Blades looked to maintain their cup pedigree.