Hull made the breakthrough in the 13th minute of action, with Diomande slotting into the back of the net from eight yards after excellent work from Grosicki.
Bolton midfielder Darren Pratley brought a fine save from Allan McGregor in the 17th minute as the visitors threatened to equalise, but less than two minutes later, Hull moved 2-0 ahead after Bowen headed a Grosicki cross into the back of the net.
The hosts might have scored a fourth just past the hour when Bowen found space in a forward position, but the attacker fired his effort over the crossbar, before Adam Le Fondre tested McGregor down the other end.
Jon Toral came off the bench in the 80th minute for his Hull debut following a move from Arsenal, but chances were few and far between in the latter stages as the Tigers eased to just their second league win of the 2017-18 campaign.
There was time for one more goal before the full-time whistle, however, with Bowen collecting a smart pass from Diomande before firing past Howard as Hull proved too strong for Bolton on the night.