Robson, the world No.45, lost 6-4 2-6 7-6 (8/6) in two hours 21 minutes to her 18-year-old opponent yesterday.
The British No.2 started well by racing into a 2-0 lead in the first set, but was immediately pegged back as Putintseva took the opener.
Robson responded well in the second set, but Putintseva held her nerve in the tie-break to book her place in the next round.
Ana Ivanovic also beat Anastasia Pavlyuchenkova 6-3 7-6 in the first round, but Sloane Stephens was eliminated in three sets to cap a miserable debut trip to the Gulf for the US teenager.
Ivanovic's career has dipped since she won the French Open in 2008.
The Serb will now play Czech Petra Kvitova or Daniela Hantuchova.