The Turkish Super Lig champions twice led thanks to stars Wesley Sneijder and Didier Drogba but Malaga responded on both occasions.
Roque Santa Cruz and Weligton Oliveira netted equalisers before Duda gave Malaga a 73rd-minute lead.
But Kazim-Richards saw Galatasaray deservedly finish with a draw as he struck in the final minute of regulation time.
Drogba thought he had opened the scoring on four minutes but his effort was ruled out for offside after calamitous Malaga defending but Galatasaray would only have to wait another nine minutes for their opener as they dominated the early exchanges.
Sneijder had threatened from range just moments earlier before a counter-attacking move led to his goal.
The Netherlands international fired a powerful right-footed curling effort into the roof of the net from 20 yards on 13 minutes.
Malaga found their equaliser in the 45th minute through Santa Cruz, who finished smartly in a one-on-one.
The La Liga club were on level terms for less than two minutes as Drogba headed in from close range to restore Galatasaray's advantage.
A Weligton header saw Malaga level once again in the 58th minute and they were ahead for the first time 15 minutes later.
Duda netted from the penalty spot before Kazim-Richards equalised in the final minute, poking in a floated set-piece.
