Darren Pratley grabbed the opener from close range, powering home a header after Chung-Yong Lee had picked him out (2).
Lee was also involved in the next goal, the South Korea international playing the ball back to Mark Davies under pressure and he fired home from 20 yards, despite Tigers keeper David Stockdale getting a hand to the ball (5).
Craig Dawson then made it 3-0 after just eight minutes, with the defender glancing home a header despite the visitors' desperate attempts to scramble the ball off the line.
Marvin Sordell made no mistake as he smashed the ball into the back of the net but the goal was awarded to Dawson.
Steve Bruce's side slowly improved after the break, with Robbie Brady having the most impact, his free-kick from a tight angle saved well by Bolton keeper Adam Bogdan.
Another set-piece from the Republic of Ireland international was then headed over from close-range by Alex Bruce.
Sordell hit the post with a shot from the edge of the box at the other end of the pitch following some good work from David Ngog.
But it was Hull who scored next, with Brady pulling a goal back with a whipped 25-yard free-kick that went through the wall and found the bottom corner (68).
That proved to be brief respite for the visitors though, with Dawson scoring his second of the afternoon as he flicked home via the post after latching onto Marcos Alonso's mishit shot (70).
Bogdan then pulled off a smart save in the closing stages to deny Brady a second goal when he pushed away his header, with the win helping Dougie Freedman's side pull further away from the drop-zone.