Marko Djokovic - ranked 868 spots below his brother - had a less successful day. The younger Djokovic, a wild-card entry into the tournament, was bounced in the opening round with a 6-3, 6-2 loss to Andrey Golubev of Kazakhstan.
A few hours before his victory, Novak Djokovic was courtside for his brother's match.
Djokovic serves as a mentor of sorts for the 20-year-old Marko and said it was hard to watch his brother struggling. The five-time Grand Slam champion acknowledged it must be difficult for Marko and his other tennis-playing brother, 16-year-old Djordje, to deal with comparisons to their elder sibling.
"In the end, he has to face this, I guess, pressure in a way for having Djokovic surname,'' Djokovic said of Marko. "All over the world where he plays tennis, I guess he has to face this pressure that is not necessary for him at this age. It's his burden, and he's very committed. He wants to succeed in tennis.''
Djokovic had not played a match in nearly four weeks - and it showed at times. He broke Stebe to go up 1-0 but had to save two break points in the fourth game as he struggled with the German's return game. Stebe pushed the set to 5-4 and deuce before Djokovic hit his first ace and another good serve which the German returned long.
Djokovic had an easier second set, breaking twice. The Serb won the match with his third ace and another serve that Stebe couldn't return.
"He definitely played well. I was impressed with his game, especially in the first set,'' Djokovic said.
Djokovic, going for a fourth consecutive Dubai title, is now 8-0 this year. He insisted he was not concerned with matching his exploits in 2011 - including three Grand Slam titles and a 41-match win streak to open the season.
"The last year was amazing,'' he said. "Definitely best year of my career. If you ask me if I can repeat it, I don't know. It's going to be very, very hard obviously.''
Sixth-seeded Mardy Fish had an easy time against Andreas Beck of Germany, winning 6-1, 6-1 to join Djokovic in the second round.
Fish broke Beck twice in the first set to lead 4-0. In the second, he broke three times before closing it out in 57 minutes.
The American has had a mixed year so far, crashing out in the second round of the Australian Open and losing to 388th-ranked Albano Olivetti in the Marseille quarterfinals last week. He did, however, help the United States rout Switzerland 5-0 in the Davis Cup.
Fish replaced Andy Roddick as the top-ranked American last year.