The visiting captain bundled home Lee Tomlin's corner in second-half injury-time to complete a remarkable comeback for lacklustre Posh, who had trailed 2-0.
Vadaine Oliver put Crewe ahead with his first goal for the club when he tapped home Bradden Inman's cross on 15 minutes.
And six minutes later, the Alex doubled their lead with their next attack.
Oliver was again involved as his tackle allowed Lee Molyneux to serge forward and his stunning through ball was calmly finished by Ajay Leitch-Smith.
Darren Ferguson's side were given a lifeline on the stroke of half-time, though, when goalkeeper Steve Phillips could only palm Mark Little's powerful shot into the path of Tyrone Barnett who lashed home from near the penalty spot.
After the break Crewe sat back on their lead and it looked like they were going to hold on.
However, after Phillips had expertly saved from Barnett, Bostwick salvaged a point with his first goal of the season.