The Alex had their first sight of goal after just 20 seconds at Gresty Road on Tuesday when Mathias Pogba crossed and Luke Murphy tested Shwan Jalal, who tipped the ball to safety.
Chuks Aneke headed wide from the resultant corner and the forward saw another effort saved by Jalal soon after.
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 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 almost made instant amends but dragged wide inside the box before Bradden Inman was denied again by Jalal.
Pogba did level 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.