Rangers made their intentions clear right from the off as they harried and hassled a Tottenham side who looked unsettled under the lights at Ibrox.
Fraser Forster made a superb save to keep out the lively Vaclav Cerny while at the other end, Jack Butland did well to deny Son Heung-min in a half the home team were on top in.
The Gers deservedly went ahead in the 47th minute through Hamza Igamane and they could have been out of sight had it not been for Forster in goal.
Just when it looked like the Scottish giants would come away with the three points, substitute Kulusevski started and finished a lovely flowing move to level proceedings 15 minutes from time.
The Spurs keeper rescued his team once again as the former Celtic man made a vital stop to keep out Cyriel Dessers' goal-bound effort late on as the points were shared.
Rangers currently sit in the eighth and final automatic qualification spot for the last 16 of the competition, with Spurs a place below them due to an inferior goal difference. Ange Postecoglou's team's winless run now stretches to five matches.