Federer began the match in style by breaking his opponent in the very first game to take control of the opening set.
However, Tursunov fought back and recovered the break of serve in the 10th game of the set to level things up at 5-5, with both players then holding serve to force a tie-break.
Federer squandered two break points in that tie-break before eventually wrapping it up at the third time of asking with a win against the serve to take it 9-7.
Tursunov struck first in the second set with a break in the third game, but the world number 30 was unable to capitalise on that as Federer hit straight back to restore parity.
Both players then held their own serve to force another tie-break, which Federer managed to win comfortably, taking it 7-2 to clinch his place in the next round.