The former world number one secured a 7-5 6-7(7) 6-2 6-4 victory on the clay court to send himself into the fourth round of the Grand Slam.
It was a tight affair between the two competitors in the opening set, with both coming close to grabbing a break point, but failing in the early exchanges.
It took the 12th game for the first break of serve to come, and it was Federer who took advantage of it to take a one-set lead.
Both players once again remained stubborn on their service games, which eventually forced the second set into a tie-break, which Tursunov edged 9-7.
Federer started the third set on the front foot by pushing Tursunov to the limit in his opening service game and eventually securing a break on the 13th point.
A further break down the line ensured that Federer was able to keep his lead and wrap up the set.
In the fourth set, Federer relinquished seven break points in one game, but eventually grabbed a crucial break of serve to give himself a 4-3 lead.
The one break was all the Swiss pro needed to ensure his place in the next round.