With his triumph on Monday, Federer, victor of the 2018 Australian Open (20th Grand Slam title) and the Rotterdam tournament, extends his winning streak this year to 14-0.
"I actually was explosive out there today and I felt good", he said.
Federer, five times victor of this tournament and defender of the title, invested less than an hour to win 6-2 and 6-1 against the number 28 in the world, reports Efe.
At one point he won 17 straight points en route to taking a 6-2, 3-0 lead, winning 10 of the final 11 games in the match.
"In Rotterdam I played five matches in a row", he said.
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"I was grateful to be out on the court after surgery that quickly but at the same time just didn't feel good at all", he added.
Federer and 10th seed Djokovic both came into the tournament seeking to become the first six-time victor of the event.
Playing for a third consecutive day due to weather delays in Indian Wells, the 36-year-old Swiss showed no sign of wear en route to a 6-2 6-1 thrashing of the Serbian in the pair's first ever meeting. Daniel plays next Argentinean tennis player Leonardo Mayer.
Japan's Kei Nishikori withdrew through illness before playing his opening match of the tournament. Cuevas was leading 3-6, 6-4, 4-2 when Thiem packed it in.
In other third-round matches, No. 7 Caroline Garcia of France beat 26th-seeded Daria Gavrilova of Australia 7-5, 6-4; No. 10 Angelique Kerber of Germany defeated No. 24 Elena Vesnina of Russian Federation 7-5, 6-2; and American Danielle Collins continued her run with a 6-4, 6-4 win over fellow wild card Sofya Zhuk of Russian Federation. Likewise, 23rd-seeded Hyeon Chung of South Korea dispatched 12th-seeded Tomas Berdych of Czech Republic 6-4, 6-4, despite 12 aces against just one double fault from Berdych.