American Taylor Fritz battled back from a set down to beat Fernando Verdasco 4-6, 6-2, 7-6 (1) - the victory ensured he has now won 11 of 12 final-set tiebreaks.
It was another snag in the return for world No. 13 Djokovic, who admitted he lacked composure while playing in just his second event of 2018 and first since having surgery.
New York Times tennis writer Christopher Clarey said the Serbian's "crisis continues" as he searches for his first grand slam title since the French Open in 2016.
'You can't really look ahead to semi-finals, finals and speculate about who you could play, ' Federer said.
The defending champion will face Serbia's Filip Krajinovic in the round of 32. It was the former world No.1's first match since returning from an injury, which forced him to undergo a surgery earlier in February.
Another love game kicked off the second set and Federer was 3-0 up before Krajinovic managed to momentarily stem the tide.
"I just struggled also a little bit with the health the last couple of weeks".
Phillies, Arrieta agree on multi-year deal
One of the wildest stats on Arrieta is that he hit homers at a greater rate (1.89%) than he allowed (1.81%) the last four seasons. Arrieta played the past five seasons with the Cubs and was a key member of the 2016 World Series championship winning team.
The Swiss maestro is unbeaten since the start of the season having won both the tournaments he has entered thus far - the Australian Open in January and the Rotterdam Open the following month. "I was actually pretty nervous playing the match", said the 25-year-old Daniel.
He had elbow surgery in Switzerland shortly after that. "Very weird", Djokovic said. "He's only going to get better from here". "Many times I have looked at the draw and, 'Oh, God, Rafa is my second-round (opponent),' or something".
On the women's side, top-ranked Simona Halep came back to top 19-year-old Caroline Dolehide 1-6, 7-6 (3), 6-2 in just over two hours.
"I think that would be a mistake".
Spanish veterans David Ferrer and Feliciano Lopez recorded routine straight-sets wins over Tennys Sandgren and Ernesto Escobedo respectively while Philipp Kohlschreiber outlasted Tim Smyczek.
Other seeded players who lost were ninth-seeded Lucas Pouille, who fell 6-4, 6-4 to Yuki Bhambri; 14th-seeded Diego Schwartzman, 7-5, 6-4 to Marcos Baghdatis; 21st-seeded Kyle Edmund, 6-4, 6-4 to Dudi Sela; and number 24 seed Giles Muller, 6-3, 7-5 to Pierre-Hugues Herbert.