Monte Carlo Masters in April, Federer wasted 15 break points.
Tursunov was trailing 0-40 in the 12th game and 7-6 down in the tiebreaker, but went on to level the match with a forehand pass down the line.
“I wish at times I could have played a bit more offensive,” said Federer, who won the French Open in 2009.
Shortly after winning the second-set tiebreaker, Tursunov appeared to have a minor meltdown while trailing 2-1 in the third. He argued with the chair umpire and took a medical timeout to treat a sore groin.
Federer next plays No. 18 Ernests Gulbis of Latvia, who beat Radek Stepanek 6-3, 6-2, 7-5.