Christie scored two minutes from time with a neat flick after Marley Watkins had made a great run down the flank and delivered the cross.
Greg Stewart pounced after 21 minutes to give Dundee the lead when he found space inside the six-yard box to connect with a Gary Harkins free-kick and nod the ball over the line.
But Billy McKay levelled the match 10 minutes after the interval when he scrambled the ball over the line from close range after Marley Watkins delivered a cross into the box.
Caley Thistle had come close to opening the scoring on 11 minutes when Josh Meekings headed against the bar from four yards from a corner.
Dundee responded when Harkins slipped a free-kick into the path of the in-form David Clarkson, but his attempt at goal was blocked by team-mate Thomas Konrad.
Clarkson was alert again as he tried to latch onto a loose pass, which forced Caley ‘keeper Dean Brill to race out and sweep the ball away before Gary Warren showed some composure in dealing with Martin Boyle’s chipped return.
Caley Thistle could have levelled the match moments before the break but Marley Watkins sent his header narrowly wide from inside the box.