Putintseva, 18, fought back after dropping her serve to win the first set, before the British No. 2 squared the match following another wayward backhand from the stocky Kazakh.
The final set lasted as long as the first two combined.
Putintseva bludgeoned her way to a double break and a 5-2 lead to allow her to serve for the match.
Robson, despondent, slumped in her chair, but her body language proved misleading as the 19-year-old reeled off the next two games to love, before breaking again to go 6-5 ahead.
Still, her Kazakh rival was uncowed, holding to love as the the world No. 101 eventually prevailed in the tiebreak.
“It just wasn’t my day — I either went for too much or too little,” a downbeat Robson told reporters afterwards, revealing she had been suffering from a chest infection all year.
Top seeds Williams and Victoria Azarenka, the world No. 1 and No. 2, are due on court today. Azarenka beat the 15-time Grand Slam winner in Sunday’s Qatar Open final.
Additional reporting by staff writer