Both sides were scarcely recognisable from the teams put out in the League last Saturday with the Bluebirds making 10 changes while even Barnet managed to bring in five newcomers.
City's skipper on the night Roger Johnson opened up the Bees in the seventh minute with a sliderule pass to Luigi Glombard but his angled shot drifted beyond the far post.
Johnson then missed a header when Kevin Cooper whipped over a free-kick as Cardiff piled on the early pressure.
But it was the visitors who shocked the home side with a freak goal on 31 minutes. Bluebirds keeper Mark Howard made a hash of a clearance which went straight to Kandol and he side-footed from 40 yards into an empty net.
Cardiff made one change at the interval with Darcy Blake replacing Rhys Weston.
Eight minutes into the second period Kandol made it two when he beat a slack home defence to head in at the far post.
City manager Dave Jones was forced to bring on Paul Parry and Joe Ledley in an effort to claw their way back into the game and immediately a snap-shot from Parry had Barnet keeper Ross Flitney scrambling low to save at the second attempt.
The changes had the desired effect of breaking City up but with veteran Paul Warhurst superbly marshalling his defence the Bluebirds rarely looked like pulling even one goal back.
City suffered a third blow two minutes from time when teenage full-back Joe Jacobson, one of the few successes in the home side on the night, was stretchered off to leave them to finish the game and the six minutes of added time with 10 men.