Goals from David Cotterill, Jamie Ward and Stephen Quinn earned the victory against a Bluebirds side reduced to nine men for an hour.
Hungarian central defender Gabor Gyepes was the first to be dismissed when he tangled with Darius Henderson in the 24th minute and Cardiff-born Cotterill slotted home the spot-kick.
The Bluebirds were then reduced to nine in the 34th minute when Ross McCormack was alleged to have elbowed Kyle Naughton near the touchline but on both occasions referee Paul Taylor was quick to brandish the red card.
One minute after the restart, poor marking by the home defence saw substitute Ward head in unmarked to put the result beyond doubt but it was not until the 87th minute that Quinn made it an emphatic win for the Blades.
"I am always happy when I come away from home and win," said United boss Kevin Blackwell.
"You have to accept these decisions and just get on with it but I thought both red cards looked harsh to me.
"When you are one on one in the box you are always likely to see a red card but McCormack was right in front of me when he was sent off and I honestly don't know why he was dismissed.
"I told the players at half-time that we had to be professional and I was pleased we scored again so early in the second half."
Once substitute Ward made it two, it was an even more one-sided contest but Kevin McNaughton was magnificent at the back for the nine-man Bluebirds and United seemed content with their lead.
With time running out and City's players visibly tiring Quinn was allowed to run un-challenged into the area and slot beyond home keeper Stuart Taylor.
"I will leave the sendings off to the 18,000 who watched the game," said Bluebirds manager Dave Jones.
"We will appeal against both dismissals and if the referee had only taken time to consult his assistant then he may have come to different decisions.
"I have watched both of them on the television and neither warranted a red card although I would have been unhappy if I hadn't been awarded a penalty when Gabor was sent off.
"At no time can you say this was a dirty game yet the referee handed out two red cards and five yellow cards.
"But even with nine men we ran our socks off and that shows we are fit not tired and ready to keep going until the end of the season."