The midfielder volleyed home Dean Ashton's cutback in the 85th minute to earn the home side a deserved point.
Ashton had given Crewe an early lead from the penalty spot after Robert Page handled in the area.
However, the visitors hit back through John Robinson's close-range effort and Alan Lee's run and shot from 25 yards before Higdon's late intervention.
Cardiff manager Lennie Lawrence
"Their's was a penalty. I was thinking if I get away with conceding a penalty here it will be the biggest let-off of my entire life.
"I realised because of the delay in it being given we wouldn't have a man sent off and fortunately we didn't as it would have been difficult for 10 men chasing round in this heat.
"It was a classic Cardiff game. Up and down, plenty of goal-mouth incident. You think you are going to come out on top and you shoot yourself in the foot in the last minute."
Crewe: Williams, Briggs, Billy Jones, Walker, Foster, Lunt,
Sorvel, Cochrane (Higdon 79), Vaughan, Ashton,
Rivers (Steve Jones 69).
Subs Not Used: Ince, Tonkin, Bell.
Goals: Ashton 5 pen, Higdon 85.
Cardiff: Margetson, Weston (Croft 87), Gabbidon, Page, Vidmar,
Kavanagh, Langley, Robinson (Collins 81), Bullock,
Earnshaw (Campbell 74), Lee.
Subs Not Used: Parry, Warner.
Booked: Vidmar.
Goals: Robinson 44, Lee 59.
Attendance: 7,339.
Referee: M Thorpe (Suffolk).