Two goals from the spot from Leigh Griffiths helped Brendan Rodgers' men past their Kazakh opponents, after grabbing a 1-1 draw in the first leg
Two stoppage-time penalties saw Celtic edge past Astana 2-1 to reach the Champions League playoff round.
Leigh Griffiths nudged the Scottish champions ahead on the stroke of halftime, but after the outfit from Kazakhstan equalized, Moussa Dembele's first goal for the club - in the 92nd minute - was required to seal the tie 3-2 on aggregate.
Despite monopolizing much of the possession, Celtic had to wait until stoppage time at the end of the first half to take the lead, when Kieran Tierney was fouled in the area.