But Swiss Bencic, making her third appearance at the Qatar Open where she made the quarter-finals last year, began her fightback in the fourth game.
The fatigue of playing into the final at the Adelaide International last week and the punishing flight to Qatar surely contributed to Bencic's visible fatigue.
Keys was more proficient in the big moments, meaning Bencic struggled in vain to steal a break, allowing the American to mop up five of the first seven games.
But Bencic bounced back when she was two games behind Keys, securing the ninth game and an ace in the 39th minute which could have helped her go level.
Keys overcame her resistance to steal the first set and her backhand side allowed her to maintain the pressure on Bencic in the second.
Keys closed out the final games with stellar serving, a superb forehand and a memorable backhand to take the penultimate game.
Her form was reminiscent of that which got her to the US Open final in 2017.
"It's amazing to be back -- I'm smiling under my mask," said Keys whose coronavirus diagnosis meant she missed the Australian Open.
She will now face Maria Sakkari who also had a good win in her first-round match.
Qualifier Laura Siegemund also pulled off an upset, seeing off Elena Rybakina 7-6 (9/7), 7-6 (7/5) having lost both her last encounters with Rybakina in 2019.
Wang Qiang, coached by Pat Cash, quickly applied pressure to Jessica Pegula during her opening service game but succumbed 6-3, 6-1.
But American Pegula fought back from several break points with defensive tennis, forcing Wang into errors with the Chinese player nonetheless scraping out an important win in the seventh game.
Wang served to stay in the set, taking it to eight games.
Wang came out of the gates fighting in the second game of the second set, achieving a break back.
Overall, Wang gave the impression of being out of sorts while Pegula consolidated her game and looked in form.
Pegula, who was making her debut in the main draw, was clinical in the closing stages of the match, dispatching Wang in just over an hour.
"I worked really hard in the (Australian Open) quarantine and got really healthy. I just decided I was going to be the mentally tough one," she said.
She will face Latvia's Jelena Ostapenko in the second round.
Tunisia's Ons Jabeur, who reached the Qatar Open quarterfinals in 2020 and is famed for self-proclaimed "crazy shots", efficiently saw off Russia's Anna Blinkova 6-2, 6-2.
Neither has won a singles title before but Jabeur is now in a position to better her Qatar quarter-final performance last year as she progresses to the second round.
Jabeur raced into the lead, buoyed by the Tunisian expats in the modest crowd, running rings around Blinkova with her deft touches.
"We love to play each other here in Doha... it's going to be extremely tough," said Jabeur of number two seed Karolina Pliskova who she will face in the second round.
Japan's Misaki Doi closed the day's proceedings, beating China's Zheng Saisai 6-4, 6-3.