First-half goals from Damien Delaney, Dean Marney and Craig Fagan saw the home side 3-0 up at half-time.
Cardiff pulled one back on 53 minutes through Michael Chopra but Michael Bridge sealed the win for the Tigers with 19 minutes left.
Hull took control of the match in the first half and had a chance early on when the ball fell to Marney on the edge of the area but his goalbound shot was deflected wide by Glenn Loovens.
From the following corner Ian Ashbee had a powering header saved on the line with Delaney sweeping in the rebound from close range to put Hull ahead.
Three minutes later the home side doubled their lead as Stephen McPhee played the ball square to Marney on the edge of the box and his left-footed effort saw the ball fly past Neil Alexander and into the net.
Hull then went further ahead on 36 minutes when Nicky Barmby cleverly put Fagan clean through on goal and he calmly skipped past Alexander and slotted the ball into the back of the net to put Hull 3-0 up.
Cardiff grabbed one back on 53 minutes when Joe Ledley put Chopra through on goal and he neatly placed the ball into the back of the net.
However, Hull restored their three-goal advantage on 71 minutes as Fagan ran in on goal from the left-hand side and fired in a shot which Alexander parried leaving substitute Bridges to slam the ball home from close range.
Moments later Hull were awarded a penalty when Fagan was brought down by Chris Gunter in the box. McPhee stepped up to take it and attempted to chip the ball into the back of the net but the ball bounced off the bar and Cardiff were able to clear.
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