Sam Vokes scored the vital goal to give Bournemouth a 1-0 win and leave their great escape still on.
This was Bournemouth's sixth win on the trot as they looked to escape from the drop into League Two, which looked hopeless even a month ago.
Bournemouth started the game nervously but Crewe could not take advantage as the Cherries nerve settled after 16 minutes with their first chance of the game.
Warren Cumming put over a cross that Shaun Cooper latched on to and headed goalwards but Ben Williams saved.
Bournemouth again went close on 18 minutes when Max Gradel crossed to pick out Vokes, who hit a right-footed volley just over the bar.
Crewe were indebted to goalkeeper Williams on 35 minutes when he pulled off a fine double save. He pushed away Gradel's ten-yard effort and leapt up as he saved the rebound from Cooper.
Bournemouth took the lead just after the break in the 54th minute through Vokes' 12th goal of the campaign.Danny O'Donnell tried to head back to his goalkeeper but made a complete hash of it. Welshman Vokes latched onto the mistake and ran through into the penalty area, before coolly despatching his left-footed shot into the bottom right-hand corner.
Crewe almost equalised barely three minutes later when George Abbey let fly with a spectacular 25-yard effort that David Forde in the Bournemouth goal did well to save.Jo Kuffour went close for Bournemouth with a spectacular overhead kick that just went over the crossbar.Kenny Lunt then went even closer with his own 25-yard effort that Forde again did well to block.
There was a few nervous moments in the five minutes of injury time, but the Bournemouth fans celebrated a vital three points that still leaves them with a chance of escaping the relegation trap door.