The Black Cats netted what turned out to be the winner midway through the first-half as 18-year-old Asoro stroked past Allan McGregor from a narrow angle for his first senior goal for the club.
Both sides ring in the changes following disappointing results
Sunderland boss Chris Coleman made three changes to the side that lost 4-0 at Cardiff City last weekend, with the absence of Didier Ndong enforced after he was given his marching orders at the Cardiff City Stadium with Lee Cattermole replacing him. Elsewhere, youngsters Ethan Robson and Asoro came into the side for Marc Wilson and Lynden Gooch.
Hull manager Nigel Adkins opted for two changes following last weekend's 0-0 draw against Reading, with attackers Nouha Dicko and Jackson Irvine making way for Evandro and former Black Cats striker Fraizer Campbell.
The hosts were the side asking most of the questions early on with the attacking duo of Josh Maja and Asoro causing problems for the Hull defence with their pace and directness.
The first chance of the afternoon fell the way of Billy Jones 14 minutes in as he was found by Asoro on the edge of the box, but the right-back lacked composure and sent his effort bobbling wide of the goal.
Asoro and Maja were Sunderland's main attacking threats in the opening 45 and the two combined two minutes later for the former to send Maja through on goal, only for the hand of McGregor to save his low shot.
Moment to remember for Asoro
The Swede would be the one to break the deadlock on 20 minutes through a fine team goal with the ball starting at the back, before a quick flurry of passes led to George Honeyman playing Asoro in behind where he made no mistake in slotting past McGregor from a narrow angle.
The Tigers began to grow into the game after being outplayed prior to Asoro's opener and looked more threatening going forward with former Sunderland man Seb Larsson whipping a few dangerous crosses into the area.
Their best chance came from a corner kick which was sent towards the penalty spot by Larsson only for Michael Hector to send his volley sailing over the bar from 12 yards.
The second period began as a more even contest, although Sunderland went close again as Bryan Oviedo sent a 25-yard free-kick skimming off the top of the net.
At the other end former Black Cat Larsson fired a 25-yard volley just wide of Robbin Ruiter's goal with the Dutch keeper scrambling, before Sunderland countered at speed and almost found a second goal as Honeyman's pull-back rolled across the line and out for a goal-kick.
Hull on top in search for equaliser
Hull were firmly in the driving seat in the second period and Sunderland had Oviedo to thank for keeping them level on 64 minutes, as the Costa Rican blocked Evandro's powerful 20-yard drive on the line with the ball headed for the top corner.
The Tigers were chasing an equaliser and perhaps should have found it through Campbell on 70 minutes, but the former Sunderland man could only fire over the crossbar from Evandro's pull-back into the area.
Asoro thought he had won his side a penalty when he under pressure from Michael Dawson with just under 10 minutes left, but referee Keith Stroud saw otherwise and showed the forward a yellow card for simulation.
Adkins went for broke late on with Hull still searching for an equaliser, throwing on strikers Dicko and Will Keane in an attempt to trouble the Sunderland backline but it was the hosts who almost made it two through Robson, but his two shots were beaten away by McGregor to keep Hull in the game.
Ruiter earned his side all three points at the death as he blocked former Sunderland midfielder David Meyler's powerful drive from six yards out, in what could prove a crucial win for Coleman's men.