Eddie Howe saluted the character of his Bournemouth side after Brett Pitman's double extended their unbeaten run to five games and sent them to the top of the League One table.
Pitman put the Cherries ahead from the spot against Crewe at Gresty Road after a dubious decision from referee Richard Clarke before Mathias Pogba levelled for the Alex. But Pitman netted the winner six minutes from time to secure a 2-1 win which saw the Cherries leapfrog Doncaster into top spot.
Bournemouth boss Howe said: "We showed real team spirit and togetherness. I think away from home it is easy to find ways to get beat but the best teams always find a way to win.
"We scored a late goal and away from home that's not always easy. Our fans were magnificent and they would have given the players a big boost at crucial times. Both sides had their moments but our 'keeper (Shwan Jalal) made some greats saves for us at key moments and we defended well."
Pitman was providing some quality deliveries for the visitors but both Josh McQuoid and Lewis Grabban were guilty of heading good openings wide. Mark Ellis went close with an effort from the edge of the box for Crewe before the home side survived a goalmouth scramble with some brave blocks.
After the break Jalal produced a superb stop to deny Ajay Leitch-Smith from eight yards and Luke Murphy rattled the crossbar with a free-kick. But the Cherries took the lead on the hour when Pogba was harshly penalised for a foul on Matt Ritchie and Pitman stroked home the penalty.
Pogba equalised in the 79th minute, crashing home Kelvin Mellor's cross with a powerful header. But Crewe were on terms for just five minutes as Pitman drilled home Steve Cook's cross for his second of the game six minutes from time.
Alex boss Steve Davis said: "I was delighted with the all-round effort and performance from our players. It was an all-round great performance but we didn't get anything from it unfortunately.
"I have told the players it has gone and to get their heads up. As long as we keep playing like that and we get better decisions from the referee we will win more games than we will lose.
"Their 'keeper made some good saves and he'd have been my man of the match just behind the referee. Our lads were magnificent. They stood up to them, really opened them up and couldn't do any more than they did."