French winger Max Gradel tormented the home defence and capped his display with two eye-catching goals in the second half.
Veteran striker Lee Bradbury had put the Cherries on their way to a feast when he headed in Danny Hollands' short corner nine minutes before half-time.
It was no more than Bournemouth deserved for a strong first-half showing and they should have gone in front in the 21st minute when Gradel squared the ball across goal for Sam Vokes but the young striker side-footed the chance straight at Ben Williams.
However, the Crewe keeper was soon beaten when Bradbury nipped in between two defenders to glance the ball home.
Williams had no chance when Gradel extended the lead just over the hour mark with a wonder goal. Bradbury, who is a key presence with his ability to hold the ball up for others, teed the Leicester City youngster up with a floated pass.
Gradel looked certain to be closed down by a couple of Crewe defenders but he hit the ball first time with his right foot from 25 yards and it flew into the top corner.
The winger got his second with 13 minutes left when he wriggled free inside the box and was given too much time to pick his spot in the bottom corner.
Darren Anderton, who had been a significant presence in the visiting midfield, tapped in the fourth with five minutes left after Jo Kuffour's shot had been turned onto a post by Williams' despairing dive.
Kevin Bond's side could have had more than the four-goal haul such were the gaps in Crewe's back line as they were forced to come forward in the second half to chase the game.
It could have been different for the Railwaymen had Ryan Lowe converted an early chance.
The striker was played through on goal by Ben Rix and, with only Neil Moss to beat, he drilled his shot the wrong side of the post. With the home fans streaming out in anger at the end, Crewe enjoyed their best spell but it was all too little too late.
Substitute Shaun Miller turned in Byron Moore's cross for a consolation goal and Chris McCready headed against the post in the closing minutes.