Kazakhstan's Putintseva, 18, fought back after dropping her serve to win the first set before the British number two squared the match following another wayward backhand from her stocky opponent.
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 and looked thoroughly beaten - 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, the world number 101 holding to love to force a tie-break, then holding her nerve in the tie-break as she took the first match point.
"It just wasn't my day - I either went for too much or too little," a downbeat Robson said afterwards, revealing she had been suffering from a chest infection all year.
Up-and-coming American star Sloane Stephens was an even higher profile casualty on the first day of play in Dubai.
The Australian Open semi-finalist - ranked 16th in the world after her fine display in Melbourne - lost 5-7 6-3 6-2 to Romania's Sorana Cirstea.
Both players had their chances in a closely-fought match, but ultimately it was Cirstea who consistently held her nerve better on the key points: she saved seven of 11 break points against her, while converting six of the 10 break points that she earned against Stephens.
The American suffered a second-round exit in last week's Qatar Open and said she had found it tough going in her first trip to the Gulf.
"It's two tournaments to a place I have never been before, a very different situation for me," Stephens said. "Some days you're going to be on court and it's not just going to turn out the way you want. Today I didn't play my best tennis, and last week I didn't play my best tennis."
The 19-year-old, who defeated newly-installed world number one Serena Williams on the way to reaching the semi-finals of the Australian Open in January, started confidently in front of a sparse Dubai crowd.
She broke in the first set to take a 5-4 lead, but then showed her inexperience, serving a double-fault on set point to allow Cirstea to make it 5-5.
The Floridian - the top ranked teenager - immediately broke again as she went on to claim the first set.
Stephens then took a 3-1 second-set lead, winning nine points in a row, but Cirstea fought back by taking five straight games to square the match.
Cirstea raced through the deciding set in 33 minutes, as the young American's serve collapsed, losing five of her last six service games.
Top seeds Williams and Victoria Azarenka - the world number one and two - are not due on court until Wednesday. Azarenka took three sets to defeat the 15-times Grand Slam winner in Sunday's Qatar Open final.
Serbia's Ana Ivanovic was forced to battle her way into the second round against Russia's Anastasia Pavlyuchenkova as she won 6-3 7-6(5).
Ivanovic's career has dipped since she won the French Open in 2008, sinking from number one in the world rankings to 13, and she was far from flawless on the floodlit Dubai court.
She was still too strong for 21-year-old Pavlyuchenkova, breaking in the first game and remaining largely in control thereafter, with her Russian opponent's forehand too often found wanting to really put her higher-ranked adversary in trouble.
"I really want to, you know, break into the top 10 again," Ivanovic told reporters. "I feel I have the game, but I just haven't been consistent enough, especially against the top players."
Ivanovic broke for a second time to go 4-1 up in the first set, a fierce cross-court return earning a break point she converted after Pavlyuchenkova thumped a forehand into the net.
Yet Ivanovic immediately lost her own serve to love as the world number 29 closed to 4-3 but the 25-year-old roused herself again, dropping only two points in the next two games as Pavlyuchenkova double-faulted to gift her the first set.
The Serb charged into a huge lead in the second set, but slipped from 4-0 up to 6-6 as her first serve percentage plunged, before winning the subsequent tiebreak 7-5.
She blamed her second set slump on a troublesome shoulder.
"I have been struggling for weeks now," Ivanovic said. "I was kind of afraid to hit the ball because it was getting a bit sore, but I was just so happy to win in two (sets) so I can regenerate more and try to be ready for the next one."
The Serb will now play Petra Kvitova or Daniela Hantuchova in the second round.
World number 11 Marion Bartoli seemed on course for a surprise exit but recovered from losing the opening set to beat Klara Zakopalova 3-6 6-4 6-1.
Bartoli will play world number one Serena Williams in the second round.
WTA Dubai first round results
Yulia Putintseva (Kazakhstan) beat Laura Robson (Britain) 6-4 2-6 7-6(6)
Ana Ivanovic (Serbia) beat Anastasia Pavlyuchenkova (Russia) 6-3 7-6(5)
Marion Bartoli (France) beat Klara Zakopalova (Czech) 3-6 6-4 6-1
Hsieh Su-Wei (Taiwan) beat Varvara Lepchenko (U.S.) 6-1 6-3
Sorana Cirstea (Romania) beat Sloane Stephens (U.S.) 5-7 6-3 6-2
WTA Bogota first round results
Paula Ormaechea (Argentina) beat Nina Bratchikova (Russia) 7-5 6-2
Mathilde Johansson (France) beat Stephanie Dubois (Canada) 6-4 2-6 6-3
2-Alize Cornet (France) beat Elina Svitolina (Ukraine) 6-2 7-6(6)
Mandy Minella (Luxembourg) beat Tatjana Malek (Germany) 6-4 6-3
WTA Memphis first round results
8-Kristina Mladenovic (France) beat Courtney Collins (U.S.) 6-3 6-1
Stefanie Voegele (Switzerland) beat Silvia Soler Espinosa (Spain) 7-6(5) 6-0
Victoria Duval (U.S.) beat Johanna Larsson (Sweden) 3-6 6-1 6-3
Marina Erakovic (New Zealand) beat Annika Beck (Germany) 4-6 7-6(6) 6-4
2-Sofia Arvidsson (Sweden) beat Jana Cepelova (Slovakia) 6-4 6-4
Jamie Hampton (U.S.) beat Garbine Muguruza Blanco (Spain) 6-3 6-3
Lesia Tsurenko (Ukraine) beat Maria Sanchez (U.S.) 6-2 6-4
1-Kirsten Flipkens (Belgium) beat Shahar Peer (Israel) 6-2 6-2