Nicky Maynard shot the Railwaymen ahead two minutes into the second half, but Kandol's first goal since November denied them. Leeds have gone seven games without a win and their promotion chances took another blow.
Crewe, winners of only two of their previous 17 matches, had the impressive Kenny Lunt back on loan from Sheffield Wednesday and fielded two players called Gary Roberts - the 21-year-old central midfielder who had emerged through the Academy and the 23-year-old winger on loan from Ipswich Town.
Leeds lacked leading scorer Jermaine Beckford through suspension, so Tore Andre Flo made his first start for a month and the veteran Norwegian shot just over the bar inside the first minute.
His striking partner Kandol also went close with two headers before having a 30-yard drive well saved as Leeds, using David Prutton in central midfield and Frazer Richardson on the right flank, enjoyed plenty of possession.
However, Crewe should have taken a 34th minute lead when home keeper Casper Ankergren failed to grab loanee Roberts' cross and Maynard spooned his shot over the unguarded net from ten yards.
Leeds had another let-off just before half-time when Lunt's curling free-kick from just outside the box thudded back off the bar with Ankergren beaten.
Crewe's reward arrived two minutes into the second half when Lunt's chipped pass enabled the younger Gary Roberts to send Maynard through and this time he made no mistake with a deadly finish from 12 yards.
Jonathan Howson should have equalised, but his half-hit shot gave keeper Ben Williams time to claw the ball away and at the other end Ankergren raced off his line to foil loanee Roberts.
However, as time was starting to run out substitute Seb Carole sent over a cross and Kandol headed home from close range.