Gudjon Thordarson had won the manager of the month award for February and he managed to steer clear of its traditional curse as his side moved further clear of the League One drop-zone.
Hereford midfielder Sam Hewson's dismissal ten minutes after the restart proved decisive although Graham Turner's side conjured a surprised equaliser with 11 minutes to go.
Crewe were good value for their win after battering the Bulls in the first half. Alex did all the running but were denied by in-form Hereford keeper Peter Gulacsi, who is on loan from Liverpool.
The woodwork also came to Hereford's rescue on three occasions including when Clayton Donaldson's powerful volley was tipped onto the near post by the keeper in the seventh minute.
Gulacsi went on to make excellent saves from Calvin Zola and Chris McCready before turning Icelandic midfield Gylfi Sigurdsson's drive around the post.
It was all Crewe but Julien Baudet ballooned a free header over as Alex failed to press home their advantage.
But when Baudet flicked on a corner after the break Hewson's trailing arm kept the ball out at the far post and referee Kevin Friend had no alternative but to send the midfielder off.
Billy Jones stepped up to send Gulacsi the wrong way from the resulting spot-kick.
Crewe failed to make their man advantage count and, with 12 minutes left, a Matt Done corner was headed back by Steve Guinan for Toumani Diagouraga to hook the ball over John Ruddy from close in.
But Hereford's parity lasted three minutes as Jones picked up a loose ball before unleashing a cracking 25-yard drive which flew into the net at the near post.