Goals from Alan Connell, an own goal from Paul Linwood and a spectacular late bicycle kick by Brett Pitman saw Eddie Howe’s side grab another deserved win.
After a scrappy opening 20 minutes when neither side could find any fluency, the game sprung to life thanks to a moment of magic just before the half-hour mark.
Connell, chasing a first league goal since April 2008, cut into the Grimsby area before curling a fine shot into the top right-hand corner.
A second followed for Bournemouth just seven minutes later, Pitman racing to the by-line before pulling back a cross which was turned into his own net by Linwood.
Grimsby, poor in the first period, surprisingly got back into the game after the interval, with Linwood converting into the same net which he had earlier scored with a looping header.
The goal brought a spell of concerted Grimsby pressure, but the last word went to the impressive Pitman as he notched an unforgettable strike.