Although both sides are out of the running to go through, it was still a competitive contest in which Frodi Benjaminsen fired the visitors in front in Astana before Nurbol Zhumaskaliyev and Andrey Finonchenko turned things around.
Faroese goalkeeper Gunnar Nielsen was kept busy in the early stages, producing two excellent saves to deny Zhumaskaliyev and Sergey Khizhnichenko.
And it was something of a surprise when the hosts fell behind after 23 minutes as Benjaminsen turned in Christian Holst's lay-off with his left foot.
However, Kazakhstan's persistence paid off five minutes into the second half when Zhumaskaliyev scored from the spot after Jonas Tor Naes' illegal challenge on Finonchenko in the area.
The home side then scored the decisive goal after 63 minutes, with Finonchenko putting the finish touch to Khizhnichenko's precision pass.
Defeat leaves the Nordic minnows without a point in the standings, while Kazakhstan are now four points better off.