At times, Federer was unplayable as he quickly found his range from the baseline and displayed delicate hands at the net.
The highlight of the match saw the Swiss star play an outrageous ‘tweener’ lob which looped over his opponent and set up an easy put away at the net midway through the second set.
After blitzing his way through the opening set for the loss of just one game, the world number eight found the going slightly tougher in the second – but a break in the seventh game ended any hope of a Becker comeback.
The only break point he surrendered came in the final game of the match, which was quickly saved before Federer reeled off the next two points to seal a comfortable victory.
"I'm extremely happy with today's match," said Federer. "Coming out and playing free tennis like that right off the bat is a good feeling.
"I know probably Benjamin has been doing a lot of travelling back and forth, Australia, Europe, America, back to Dubai, back for Indian Wells and Miami, but you've got to take advantage of that. I have been here for some time. I had a good preparation. I'm happy it paid off thus far."
"It's hard to complain when you win, but I think there is quite a few things that I could have done better," said Tursunov.
"But, given the circumstances, I would rather play bad and win than play great and lose. It gives me another chance to play better than today. I'm going to be Mr. Positive today."
World number two Novak Djokovic begins his quest for the Dubai title on Tuesday with a first round match against Uzbekistan’s Denis Istomin.
ATP Dubai - Round One Results
4-Roger Federer (Switzerland) beat Benjamin Becker (Germany) 6-1 6-4
Roberto Bautista (Spain) beat Adrian Ungur (Romania) 6-1 6-3