The world number two lost his opening two service games and struggled with the German's big serves in the early exchanges.
But the Serb rallied in determined fashion to eventually take the first-round match 7-6 (7/1), 6-3.
"It wasn't a great start, I was 1-5 down, it didn't look very good," Djokovic said after winning in just under 90 minutes.
He attributed his slow start to early-season rustiness rather than any long-term concerns over his form, following a relatively poor second half of the season in 2016.
"I guess I had to get more time to get the engine started. It's the first match of the year, you never know how you're going to start.
"I mean, I was a bit flat on my feet, and Struff, credit to him for playing aggressive, hitting the serves well, and ripping (the) ball from the baseline.
"But I stayed composed because I knew, I believed that I could find the rhythm, start reading his serve better, and that's what happened."
Djokovic, who is the defending champion in Doha, hit 17 winners but also 20 unforced errors.
In total, his opponent thundered down nine aces.
The 12-time Grand Slam winner is looking to reclaim his number one ranking from Andy Murray, who is also in Doha, and is the tournament's number one seed.
If matches go to form the rivals will meet in a mouthwatering final on January 7.
Before the tournament, Murray said Djokovic would be his main rival this season, but the Serb said 2017 would be about more than two players.
"We have the return of (Rafael) Nadal and (Roger) Federer that we cannot count out in any circumstances because of their history and results and the quality of players that they are," he said.
Also on Monday there were victories for Dustin Brown, who edged past Argentina's Facundo Bagnis in three sets in the first round of the singles, 6-1, 6-7 (2/7), 6-4.
And number four seed, Belgium's David Goffin, who beat Murray in an exhibition event in Abu Dhabi last week defeated Robin Hasse of the Netherlands, 7-6 (7/4), 6-2.
Murray's begins his attempt to win the Qatar Open, an event he last won in 2009, with a first-round match against France's Jeremy Chardy on Tuesday.
The newly knighted Scotsman though was in action in the doubles on Monday, but he and partner Mariusz Fyrstenberg lost in straight sets to David Marrero and Nenad Zimonjic.