"I'm extremely happy with today's match," Federer said. "Coming out and playing free tennis like that right off the bat is a good feeling."
The eighth-ranked Federer has never dropped a set to the 93rd-ranked Becker in four matches.
Federer and top-seeded Novak Djokovic, who will play his first match on Tuesday, have won nine of the last 11 titles here in Dubai.
Federer raced through the first set against Becker in 22 minutes.
"Things can run away very quickly here," Federer said. "If you look at the winner list from here, it's guys who play well on (fast) grass courts.
"It's worth it to go for your shots and you feel like risky tennis will be rewarded."
In the second set, Becker challenged better by playing himself into points.
Federer faced a break point in the final game, which went to deuce twice, but managed to close it out.
Seventh-seeded Philipp Kohlschreiber of Germany won his opening match 6-3, 6-3 over Dutch qualifier Thiemo De Bakker.
Kohlscreiber led 6-3, 5-0 when he lost three game in a row before serving out.
Eighth-seeded Dmitry Tursunov of Russia was a 7-5, 6-1 winner over 101st-ranked qualifier Lukas Lacko of Slovakia.
"I just tried to keep fighting," Seppi said. "I didn't have so many matches under my belt this year. He gave me some chances to come back."
The victory was only the second for Seppi this year. His only other match win was beating Lleyton Hewitt in five sets in the Australian Open first round.