The Swiss, six times the champion in Melbourne, never faced a break point in the match as he remained undefeated (20-0) in first round matches at the year's first major.
Federer breezes through opening set in clinical fashion
It was always going to be a tough proposition for Istomin, now ranked 101st in the world and although he saved a break point in his opening service game, he pulled a forehand long when down 15-40 to hand Federer a 3-1 lead.
Despite only getting 56 percent of his first serves in play, the Swiss was untouchable on his delivery, losing just two points in the opening set. A love hold made it 5-2 and after Istomin posted a hold of his own, the world number three closed out an efficient first set with a forehand winner.
Early break gives Swiss two-set lead
The Uzbek, conqueror of another six-time Aussie Open winner here, Novak Djokovic, was again behind quickly in the second set after getting broken in the third game after dumping a forehand into the net. He would get to deuce on Federer's serve in the sixth game, but couldn't progress any further.
After saving a break point to avoid going down a double break, Istomin held and picked up his first love hold in his next service game to stay in touch at 5-4. It wasn't enough to make a difference as Federer blasted an ace on set point.
Federer closes out match in straight sets
The third sat began with Istomin saving a break point to battle his way to a hold. Unlike the previous two sets, he held in the third game to take a 2-1 lead, but that advantage was short lived as Federer converted his third break point with a classic forehand return-volley winner combination.
Ahead 3-2, the Swiss legend was untroubled on serve the rest of the way and held a match point on Istomin's serve in the ninth game, the Uzbek doing well to save with a big serve, eventually holding. It only delayed the inevitable as Federer closed out matters on his second match point.