Federer trailed 4-2 in the deciding set before levelling at 4-4.
The 20-time Grand Slam winner then saved match points in the 12th game before sweeping through the tiebreaker to record his 1,200th career win.
Federer, playing his first clay court tournament in three years, will face Austrian fifth seed and recent Barcelona champion Dominic Thiem on Friday for a place in the semi-finals.
