The scoreline suggested a cruise for the Serbian top seed, but it was anything against the Ukrainian and he had to save four break points on his way to securing victory in 84 minutes.
"It wasn't as easy as the scoreline indicates," said Djokovic. "I needed to work for my games. My serve worked really well in the second set, and that helped me to get some free points.
"But having not played for more than four, five weeks, an official match, obviously it takes its toll on the court.
"I practised a lot. I put in a lot of hours on the court, trying to develop my game, trying to get myself in the right shape, and it's going to click sooner or later."
Djokovic has won the title in Dubai four times previously and has only lost three matches there.
"The atmosphere is great. I enjoy it," said Djokovic, who is bidding to win his first title of 2014. "It's a beautiful stadium. I have had lots of success on this court, at this tournament, and I always look forward to coming back."
Joining Djokovic in the second round are Tomas Berdych and Jo-Wilfried Tsonga, the third and fifth seeds respectively.
"I see myself continuing to work, continuing to improve my game," said Tsonga. "Nobody knows what will happen in a few weeks. So I keep fighting. I stay confident. This is the key."
But there was despair for Juan Martin Del Potro, seeded second in Dubai, after he was forced to retire with a wrist injury midway through his match against Somdev Devvarman of India.
The big Argentine lost the first set 7-6(3) before throwing in the towel, and he later admitted he may need surgery to rectify the problem - four years after going under the knife with a similar problem.
Dubai Championships results
1-Novak Djokovic (Serbia) beat Denis Istomin (Uzbekistan) 6-3 6-3
Somdev Devvarman (India) beat 2-Juan Martin Del Potro (Argentina) 7-6(3) 0-0 (Del Potro retired)
5-Jo-Wilfried Tsonga (France) beat Victor Hanescu (Romania) 6-2 6-4
6-Mikhail Youzhny (Russia) beat Michal Przysiezny (Poland) 6-3 6-4
Nikolay Davydenko (Russia) beat Andrey Golubev (Kazakhstan) 7-6(6) 6-4
James Ward (Britain) beat Teymuraz Gabashvili (Russia) 2-6 6-4 7-6(6)
Sergiy Stakhovsky (Ukraine) beat Ivan Dodig (Croatia) 7-6(6) 6-7(4) 6-2
Malek Jaziri (Tunisia) beat Igor Sijsling (Netherlands) 0-6 6-4 7-6(4)
Radek Stepanek (Czech Republic) beat Michael Russell (U.S.) 5-7 6-3 6-1
Lukas Rosol (Czech Republic) beat Daniel Brands (Germany) 7-6(4) 6-4