The reigning champion surged into a two-shot lead after first-round leaders Rory McIlroy and Shane Lowry could only card rounds of 70 and 71 respectively at the Jumeirah Golf Estates in Dubai.
World number one McIlroy, competing for the first time in six weeks after taking time out to prepare for an upcoming court case with his former management company, finished the day in a three-way share for second, level with Richie Ramsay and Danny Willett on eight under.
The biggest mover of round two was Spaniard Rafael Cabrera-Bello, who shot a stunning 64 to climb 35 places and to within three strokes of Stenson.
A six-foot birdie at the first set the tone for Stenson's round, with another shot picked up at the second on his way to a two-under front-nine score.
The Swede accelerated on the back nine, sinking four birdies to climb to the summit of the leaderboard.
McIlroy and Lowry went out in the final pairing and, despite modest scores, provided some of the day's best entertainment.
The Northern Irishman endured an eventful final five holes, with three birdies and a bogey, while at the 18th he scrambled par after finding water off the tee.
Playing partner Lowry, meanwhile, made a dreadful start and was two over after four holes, but a hole-in-one at the par-three 13th produced a memorable highlight.
McIlroy took some comfort from his last-nine showing and backed himself to perform well over the weekend.
"I started to hit some better shots on the back nine and [on Saturday] I'm sure I'll start to hit a few more," he told the European Tour website.
"I'm happy with where I'm at, there's still 36 holes to play."