The tournament's 32 seeds all received first-round byes.
Djokovic is a 12-time Grand Slam champion and former World No 1 but was only seeded 10th here, having taken six months off after Wimbledon previous year and then undergone surgery following a fourth-round loss at the Australian Open.
Verdasco's first serve proved almost unplayable in the deciding set of the second round match as he improved his career head-to-head record against Dimitrov to 2-2.
"Very weird. I completely lost rhythm", admitted the Serb. Just struggled also a little bit with (my) health the last couple of weeks. Even though I served my five aces yesterday, none today. While he targeted a comeback at the Madrid Masters in May, his quick recovery encouraged him to play at Indian Wells. In the summer of 2006, Federer claimed Wimbledon and Canada Masters titles before Andy Murray beat him in the second round of Cincinnati, the fifth and last loss he suffered that year. Daniel broke midway through the third set and never looked back, closing out his first Top 20 win with aplomb.
"I just came to understand how I had to play against Lleyton". He will look forward to using these tournaments as a springboard before the clay-court season begins, where he will be hoping to have a deep run at the French Open to win the 13th Grand Slam of his career.
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While Federer was far from ideal, he did improve to an unblemished 13-0 on the year and took the next step in snaring his third title of the young season.
In a rain-affected encounter that saw the match start on Sunday (AEST) and resume on Monday, the players were forced off the court due to rain in the second set with the score even at 2-2. It was actually quite interesting. You know, the nighttime is much more deader. The surface doesn't react so much; the ball doesn't travel so fast.
"It feels insane. I mean, I'm still in shock", Anisimova said.
Federer won the Indian Wells championship for a fifth time past year, adding to his crowns in the Southern California desert in 2004, 2005, 2006 and 2012.
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Eighth seed Jack Sock, 18th seed Sam Querrey, 32nd seed Milos Raonic all progressed into the third round.
Gael Monfils beat the 15th seed John Isner 6-7 (5), 7-6 (3), 7-5; Pierre-Hugues Herbert beat the 24th seed Gilles Muller 6-3, 7-5 and Dudi Sela prevailed over the 21st seed Kyle Edmund 6-4, 6-4.
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World No. 3 Marin Cilic also won on Sunday, defeating Hungary's Marton Fucsovics in straight sets, 7-5, 6-3.
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