The fourth-ranked Federer took time to find the rhythm in his ground strokes, and saved a break point at 5-all before winning the first-set tiebreaker.
The 30-year-old Swiss then broke the 54th-ranked Starace's serve in the opening game of the second.
Federer last played on Sept. 18 in a Davis Cup match on grass in Australia where he beat Bernard Tomic in four sets.
After opting to rest and recharge, Federer played his first match ranked outside the top three since winning the 2003 Wimbledon title as the No. 5.
Federer came in with a 5-0 career record against Starace, but was unable to put pressure on the Italian right-hander's serve in the first set.
Starace created the only break point in the set which Federer saved with a forehand winner.
Federer converted his first set point in the tiebreaker by hitting a forehand winner down the line.
Leading 5-3 in the second, Federer earned a first match point with an overhead backhand volley winner, but then netted a service return.
He clinched the match in the next game with a service winner.
The 113rd-ranked Kukushkin entered the main draw after 30th-ranked Jurgen Melzer of Austria pulled out due to a season-ending back injury.