Hull had taken a first half lead through Matty Fryatt. After the break Joe Ralls on his debut levelled and then came the penaty incident. Soon after Nick Bamby scored the decisive goal that won Hull the three points.
"Nick has always had a very positive impact for us," Hull boss Nigel Pearson said. "He is a player who brings quality to the team.
"We're not just a squad of young players but our young players have great potential, and Nick is a role model for them.
"During the week he's more of a player than a coach, but this is his club and it means a lot to him.
"The most important thing for me is that I know he can still perform. He's not just a cosmetic extra.
"There are lots of teams that will think they have a chance, but we've made some great progress," Pearson said.
"The players can be very pleased with their performance and there is an air of confidence about them."
Cardiff felt aggrieved after referee Webster performed a U-turn on a decision to award a penalty to the visitors after Jack Hobbs' trip on Filip Kiss.
The referee, after consulting his assistant, signalled for offside, and Barmby notched the winner moments later.
"He was clearly offside so it wasn't a fractional thing," Pearson added.
"Common-sense prevailed and it would have been unjust to have conceded at that point."
However, Malky Mackay was dismayed by what he called a "game-changing decision".
The Cardiff boss said: "The linesman has apologised for not putting his flag up, but that makes no difference to me. The play went on into a second phase and if it was offside it was marginal."
"Kenny Miller suffered a groin problem in the first minute and we had to restructure and put square pegs in round holes," Mackay added.
"But I thought we were good enough value to get something out of the game."