Crystal Palace boss Iain Dowie was fuming after his high-flying outfit failed to wrap up a one-sided encounter in the second half.
Crewe, reeling after a 6-1 thrashing at Cardiff last Saturday, started well with a new strike-force of Higdon and Steve Jones.
And it was Steve Jones who gave them a seventh-minute lead when he took his strike partner's deflected pass and accelerated into the box to shoot past Gabor Kiraly.
Higdon should have added to the Railwaymen's lead when he flicked a header wide from Kenny Lunt's cross, when the goal was at his mercy at the back post.
It took a while for Palace to warm-up but when they did their midfielder Ben Watson was often at the centre of their play. He came close with a flying volley which home goalkeeper Ben Williams did well to turn the ball round the post.
And Williams was tested by a firm header by Darren Ward from a Danny Butterfield cross on 32 minutes.
Their was another scare for the hosts when captain Lunt had to clear off his line when Michael Hughes' in-swinging corner evaded everyone and looked to have gone in at the far post.
Hughes provided the supply line for Dougie Freedman to equalise in the 52nd minute. The Scot's connection on the end of the Northern Ireland international's cross was far from clean but it managed to carry past Williams into the far corner.
Clinton Morrison put the visitors in front 13 minutes later when he tucked away a neat near post header from substitute Gary Borrowdale's pullback from the byline.
However, Crewe staged a late rally. Substitute Luke Rodgers almost connected with Gary Roberts' cross and substitute goalkeeper Julian Speroni produced a stunning save to keep out a curling Lunt free-kick.
Morrison should have sewn things up for Palace but he lifted Freedman's pass over the bar from six yards out.
Crewe took advantage of the seven minutes of added time, due to the injury to Kiraly which forced the Hungarian off on the hour mark.
When Steve Jones whipped the ball across deep into injury-time Higden was there unmarked to head home the equaliser.