The Croatian struggled to match Federer, who won 10 of the final 11 games in the match and at one point even won 17 straight points as he won the first set 6-2 and raced to a 3-0 lead in the second.
It was another snag in the return for the world number 13 Djokovic who admitted he lacked composure while playing in just his second event of 2018 and first since having surgery.
Earlier, Japan's Kei Nishikori said he had withdrawn from the BNP Paribas Open at Indian Wells through illness. Less than 24 hours later, he was back on the court, where he finished off Federico Delbonis 6-3, 7-6 (6).
Djokovic was beaten 7-6 (7-3), 4-6, 6-1 by the 25-year old qualifier in his first competitive match since losing in the last 16 at Melbourne.
Djokovic underwent right elbow surgery after falling in the fourth round of the Australian Open in January.
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"Filip's wasn't so good and then things go quickly", Federer told Sky Sports in a post-match interview. "Very weird", Djokovic said.
Djokovic took six months off after Wimbledon previous year and returned in January's Australian Open where he lost in the fourth round.
The 36-year-old marvel continues to defy the ageing process as he needed just 58 minutes to overpower the Serb with a brilliant display of Swiss timing.
Djokovic had four aces but overall he served poorly making four double faults and winning just 65 percent of his first-serve points.
He had elbow surgery in Switzerland shortly after that.
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"When you do come back from injury or when you haven't played in a long time, it just takes extra effort. He's only going to get better from here".
Gael Monfils upset number 15 seed and 2012 runner-up John Isner 6-7 (5), 7-6 (3), 7-5.
The ex-world No. 1 says he is yet to find his rhythm in practice as well but is glad he recovered sooner than expected from his surgery and that he managed to get on a match court this week.
The win sets up a third-round showdown with Spaniard David Ferrer, who defeated Tennys Sandgren of the United States 6-2, 7-6 (7-3).
Next, he'll see Jeremy Chardy, an unseeded Frenchman who beat countryman Adrian Mannarino, 7-5, 4-6, 6-1 in a morning match Monday.
Arrieta to sign with Phillies
Likewise, the Phillies needed a veteran presence on their starting rotation and they found it at a team-friendly cost as well. Arrieta will lead a Phillies staff that includes Aaron Nola , who has already been named Phillies' opening day starter.
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