The visitors took the lead through Marko Devic’s stunning half-volley but had captain Oleg Kuzmin sent off for a second yellow card soon after.
Kuzmin opted to bundle over Can as the German tried to power past him down the wing. The referee had no option but to give him his second yellow.
The red card seemed to have paved the way for a whitewash in favour of the reds as Liverpool soon equalized.
Divock Origi nodded down Philippe Coutinho’s free kick for Emre Can to fire home from close range the first goal of the Klopp era.
However, after the goal, Liverpool pressed for the entire second half but struggled to truly test Sergei Ryzhikov in the Kazan goal.
Liverpool were limited to half chances in an ultimately difficult evening for Klopp and Liverpool as they struggled to break down their opponents for large periods of the match.
Christian Beneteke came on to add some power upfront but hit the post in the final 10 minutes as Liverpool were held to a third successive Group B draw.
The Russian visitors would have earned some credit for keeping their discipline in a difficult away match.
Liverpool have kept just one clean sheet in seven games at Anfield this season – against Bournemouth in August.