Former Chelsea and Arsenal defender David Luis joined Pafos in August
Karait Almaty were unable to claim their first-ever Champions League win despite playing against 10 men for the majority of their goalless draw against Pafos.
Pafos' plans for their own first victory in the competition were dealt a huge blow when Joao Correia was sent off after just four minutes.
The Cape Verde international booted Luis Mata in the face with an outstretched, high leg and English referee Chris Kavanagh was quick to reach for his red card.
Vlad Dragomir thought he had found the winner for Pafos in the 72nd minute when his shot from long range hit the crossbar and bounced in off the back of Kairat goalkeeper Temirlan Anarbekov.
But it was ruled out for an offside in the build-up and Ofri Arad hit the woodwork for the Kazakh side moments later as both sides chased a winner.
Despite being reduced to 10 men, the Cypriot champions had the best chance of the opening half when captain Dragomir rushed clear on goal, only to smash his shot straight into Anarbekov.
The visitors continued to threaten after the break, with Kairat captain Aleksandr Martynovich forced into a goalline clearance, while Anarbekov made a fine fingertip save to deny David Luiz.
The former Chelsea and Arsenal defender then missed a golden opportunity with just over 20 minutes remaining as he poked the ball straight at the Kairat keeper.
Kairat are 33rd in the 36-team league phase table and will travel to Inter Milan for their next Champions League fixture on 5 November, while 26th-placed Pafos host Spanish side Villarreal the same day.
Watch highlights of every Champions League game from 22:00 on Wednesday on BBC iPlayer and the BBC Sport website and app.
There will also be a Champions League Match of the Day on BBC One on Wednesday, from 22:40 to 00:00.
