It only took seconds for Cardiff to open the scoring. Tony Capaldi found McPhail deep in the Hull half of the field and the midfielder turned and clipped a shot against the underside of the crossbar and into the net.
The Bluebirds were quicker on the ball than play-off hopefuls Hull and, when McPhail flipped a pass to Thompson, his goalbound shot was palmed away by Boaz Myhill.
Richard Garcia had Peter Enckelman diving to push behind a fierce drive as Hull finally found some attacking options, but the ball was swiftly moved back down the field.
An injury to Kevin McNaughton meant a change for the Bluebirds and he was replaced by Joe Ledley three minutes before the break.
It was the Tigers who began the second half on top and for a long time the Bluebirds were pushed back on defence.
In the 55th minute, Glenn Loovens was forced to hack over his own goal as Craig Fagan moved in.
Then Tigers skipper Ian Ashbee went for goal but Enckelman stooped to save as the visitors continued looking for an equaliser.
The Bluebirds mounted an attack in the 69th minute but Sinclair's shot rose high over Myhill's crossbar.
A piece of Peter Whittingham magic almost conjured up a goal in the 78th minute but Myhill managed to tip behind for fruitless corner.
That was a rare Bluebirds attack and the match came to an end with them defending desperately as Hull went forward in numbers.