The Bluebirds had seen their lead over third-placed Bristol City cut to one point earlier in the day, but Sol Bamba's goal shortly before the hour mark proved to be enough to restore their cushion in the automatic promotion places.
The hosts took just 10 minutes to create their first chance of the contest when Nathaniel Mendez-Laing's run created space for Loic Damour, but the midfielder could not hit the target with his effort.
Neil Etheridge in the Cardiff goal was called into action for the first time after 18 minutes when he denied Nouha Dicko, but the hosts needed the woodwork to come to their rescue midway through the first half when Dicko again came close.
The Hull forward collected the ball in the box before unleashing his shot on the turn, but his effort came back off the foot of the post.
Allan McGregor's first meaningful save of the match arrived on the half-hour mark when Lee Tomlin was denied, and the Cardiff man squandered another sight of goal with five minutes remaining of the half when he sliced a volley narrowly over.
Cardiff were beginning to pose more of an attacking threat at the end of the first half, and they quickly picked up where they left off at the start of the second too when Junior Hoilett nodded wide from close range after Bamba had flicked Joe Ralls's free kick on.
Bamba made no such mistake when presented with a similar chance himself just before the hour mark, though, heading in after Anthony Pilkington had got an initial touch to Tomlin's cross.
Hull struggled to produce any immediate response to falling behind, with a Damour effort which went wide 20 minutes from time their main sight of goal heading into the closing stages.
However, Etheridge was forced into an important stop to deny the visitors an equaliser with just five minutes remaining when Ondrej Mazuch almost rescued a point for Adkins's side.
The Tigers have made an unwanted habit of conceding goals late on in matches so far this season, but they could not score one this evening as Cardiff held out for a win which keeps them equidistant between first and third, extending their unbeaten home record in the Championship this season.
Hull, meanwhile, have now won just one of their 11 Championship outings on the road so far this term and drop down to 19th place as a result of the defeat, now only five points clear of the relegation zone.
Cardiff (4-4-3): Etheridge; Peltier (Paterson, 82'), Ecuele Manga, Bamba, Bennett; Tomlin (Halford, 83'), Ralls, Damour; Mendez-Laing, Pilkington (Bogle, 68'), Hoilett
Hull (4-2-3-1): McGregor; Tomori, Dawson, Mazuch, Aina; Hector, Larsson, Toral (Bowen, 64'), Irvine, Grosicki; Dicko (Diomande, 67')