Despite conceding the first set, Russia's Kuznetsova put up a spirited defence in the second leading to increasingly sprawling rallies with her well-matched Belarusian opponent.
A number of knife-edge line calls added to the suspense as the two played into the evening, prolonged by Kuznetsova's formidable depth and court coverage in the second set.
Azarenka's composure slipped in the seventh game of the second as she failed to capitalise on several break points, swearing loudly towards her coach.
"I definitely missed the last six years I wanted to come (to Doha)," said two-time Doha champion Azarenka.
"We've been playing against each other for so long," she said of her familiarity with Kuznetsova's powerful style of play.
Seventh seed and Australian Open finalist, America's Jennifer Brady, succumbed 6-1 6-2 to Estonia's Anett Kontaveit who has only progressed as far as the second round at the last two editions in Doha.
Kontaveit kicked off the tournament by applying significant pressure on Brady in the opening exchanges, setting the stage for an upset under the cloudy Doha sky.
Brady, who had won nine of her last 11 matches prior to Doha, struggled to get into her stride with the Estonian dominating the opening set, repeatedly forcing Brady off balance.
'Very tough match'
"I watched Jennifer's journey at the Australian Open... I was expecting a very difficult match and I'm very pleased to get to the second round," said Kontaveit.
Kontaveit was one of the players forced into two weeks of strict quarantine in Australia ahead of the Open at which she lost to Shelby Rogers in the third round.
"It wasn't easy and it wasn't something we'd done before," she said.
Russia's Veronika Kudermetova tested her Spanish opponent, world number 15 Garbine Muguruza, but ultimately slipped to a 6-2 7-6 defeat.
The Spaniard was a quarter-finalist in Qatar in 2020, losing to Ashleigh Barty who is absent from this year's tournament, and once again advances to the second round.
Her imposing 1.8 metre presence on the court helped her assert dominance over Kudermetova in the first set.
She fended off several break points against her serve, helping to avoid her clash against the Russian going the distance like their last tussle in Dubai.
Muguruza won a hard-fought tie-break for the second set despite initially falling behind, eliminating the need for a third -- and a re-run of Dubai.
She will now face reigning Doha champion Aryna Sabalenka in the second round.
"I was expecting a very tough match," Muguruza said.
Latvia's Jelena Ostapenko put in one of her best performances of recent months, undoubtedly capitalising on Kiki Bertens' recent achilles surgery, thrashing her 6-0, 6-2.
In October Netherlands' Bertens posted a photo of herself in hospital with a cast on her left leg shooting a smile and thumbs up at the camera, writing that achilles pain had "bothered me too much lately in training and games".
She was playing for the first time since the French Open and did not get into her stride for the duration of the match, although did manage a string of points before succumbing.
"The foot was fine today so I think that didn't affect me at all," said Bertens. "But I think I didn't have match readiness getting into today. Jelena was playing really well."