Djokovic opened his defence of the title with a comfortable 6-3 6-3 win over France’s Michael Llodra.
Federer, the top seed and four-time champion, beat India’s Somdev Devvarman by the same 6-3 6-3 scoreline.
Both will face Spanish opposition in the second round, with Djokovic to take on Feliciano Lopez while Roger Federer will meet Marcel Granollers.
Djokovic was barely troubled by Llodra, who beat the Serbian at their previous meeting at the Paris Masters in November.
Choosing to serve and volley at every opportunity, Llodra provided an easy target for Djokovic to pass, with the Frenchman missing a number of balls at the net.
After holding a break point in the opening game, Djokovic broke to lead 3-2 when Llodra made a backhand error, and he closed out the set with a second break at 5-3.
Djokovic then broke for 3-1 in the second set with a superbly struck winner down the line and, after recovering from 0-40 to hold for a 5-2 lead, he claimed victory with a second serve ace.
“I didn’t know how I was going to start the tournament after three weeks of not playing an official match, so I have to say I’m happy with the performance today,” Djokovic said.
“It’s not easy after playing 23 years from the baseline you want to step into the court and go to the net a little bit. But I’m working on that variety in my game, using the serves well, and I did well today.”
Like Djokovic, Federer was playing his first game since the Australian Open and there were some signs of rustiness from the former world number one in the opening exchanges.
But Devvarman was unable to cause the Swiss any real moments of concern, as Federer saved the only two break points he faced.
Moreover, he brought a packed centre court crowd at the Aviation Club to its feet with some stunning winners.
“I’ve had some tough early round matches here in the past so the last thing I was going to do was underestimate Devvarman,” said Federer.
Seventh seeded Cypriot Marcos Baghdatis lasted only 23 minutes against Andrey Golubev, losing the first four games before retiring with illness, and Serbian sixth seed Viktor Troicki was beaten 6-1 7-6 by Philipp Kohlschreiber of Germany.
Nikolay Davydenko has been struggling of late, but the Russian took just 57 minutes to overwhelm Guillermo Garcia-Lopez of Spain 6-2 6-0.
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Djokovic And Federer Into Second Round In Dubai