On-loan striker Neil Harris gave the visitors the lead before Graham Kavanagh was sent off as the first half burst into life in the closing stages.
But after going a man down the Bluebirds could not hold on and Liddell levelled before Gray grabbed the winner as the Blades dominated the second half.
United midfielder Michael Tonge and Cardiff's Chris Barker traded early long-range efforts as both teams made a lively start.
Harris, making his first start since signing from Millwall, was expected to replace Cameron Jerome in attack, but Bluebirds manager Lennie Lawrence decided to play both and they combined well in the fifth minute when the teenager nodded Harris' cross wide of the upright.
Lawrence's side only boast one away win in the Championship, a 3-2 triumph at Wolves in September, and they were keen to give their travelling fans something to shout about as Darren Williams and Kavanagh tried their luck from distance but neither had the accuracy to trouble Ian Bennett in the home goal.
Neil Warnock's side were finding it difficult to get beyond a stubborn Cardiff rearguard although Jon Harley found himself with the time and space to let fly from the edge of the area but Bluebirds keeper Tony Warner easily held on.
Harley should have done better and it proved to be a costly miss as the visitors gained the upper hand five minutes before the break.
Peter Thorne played Harris in on the left and he made no mistake, firing the ball into the bottom corner but his side went a man down just a minute later when Kavanagh was dismissed for a wild lunge on Harley.
Lawrence was forced into a reshuffle at the break and Jerome made way for midfielder Joel McAnuff, while Warnock brought on Danny Cadamarteri and Andy Liddell for Paul Shaw and Derek Geary.
The Blades took the game to their opponents from the start of the second half with Alan Quinn sending a free-kick wide of the target before Liddell's effort from the left was held by Warner.
Tonge went closest to hauling his side level when he crashed a fierce drive off the woodwork with just over an hour gone and Gray was denied by Warner just a minute later.
But the home fans did not have long to wait and the pressure paid off in the 69th minute when Liddell slotted home following a clever pass from Tonge.
United kept pressing and Gray turned the game on its head when he blasted home from close range with 10 minutes left and the 10 men found no way back.