Michael Dacosta Gonzalez netted a hattrick, while Ameer Ali, Eugene Nyarko and Jonny Day all got themselves on the scoresheet at Highbury Stadium.
Bournemouth made the worst possible start as their hosts took the lead inside three minutes through skipper Owen Devonport, who finished confidently from inside the box.
But the Cherries responded well to the early setback.
Ali scored the equaliser in the 11th minute as he applied the finishing touch after a good team move.
Moments later, the early comeback was completed as Dacosta Gonzalez powered home from 25 yards to make it 2-1.
Bournemouth were now in control and applied the pressure, and their third goal came after 26 minutes, when Nyarko was slid through by Koby Mottoh and he finished with composure.
Alan Connell’s side was relentless and made it four when Dacosta Gonzalez scored his second from the top of the box after good work from Mottoh.
Shortly before halftime, it was five when Ali played Day in, he went one-on-one with the keeper and did the rest to finish and complete a brilliant first half showing.
Fleetwood came out of the blocks in the second half well and scored their second to close the gap a little, as Alfie Kelly headed home.
But they weren’t able to break down the Cherries defence further, and the four-goal advantage was restored in the 71st minute.
Dacosta Gonzalez completed his hattrick when he finished well after a good set piece routine from the Cherries.
That completed the scoring for the game as Bournemouth recorded an emphatic 6-2 away win, as they responded well to a 1-0 defeat to Charlton Athletic on Good Friday.