"I was attacking when I had my chances and controlling most of the times the points", said Cilic.
On Krajinovic, Federer said: "I still think he can play much better than he did today". After another 90-minute delay organizers suspended play for the night.
Daniel, speaking on the biggest win of his career, said, "It's kind of hard to describe.I can't believe I beat someone like that on the center court like this; it's insane".
Despite the promising outlook, Federer insisted he was taking it one match at a time.
Krajinovic reacted well to Federer's first blow, breaking back immediately after going 2-0 down at the beginning of the match. For the first time in six years, Federer has entered a tournament as the world's No. 1 player.
Djokovic said he felt like it was his "first match" on tour and was unable to explain his opening set stumble or his capitulation in the decider.
On his return from right elbow surgery, Djokovic looked a pale shadow of his former self as he went down 7-6 (3) 4-6 6-1 to make a quick exit from a tournament he has won five times. He lost to Chung Hyeon in the Australian Open fourth round in January before undergoing the surgery.
Djokovic scrambled to win the second set but looked rusty on stadium court, making 62 unforced errors compared to 29 for Daniel.
The Melbourne event was Djokovic's first since Wimbledon last summer, as he was sidelined due to the elbow ailment that ultimately led to the operation.
"I was feeling like he was not loving my slice and I was also mixing in drop shots", said Federer who extended his flawless record this season to 14-0. "When you go away from the game for over a two-month period it starts feeling a little bit that way".
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.
Gael Monfils upset number 15 seed and 2012 runner-up John Isner 6-7 (5), 7-6 (3), 7-5.
Argentina's del Potro, who is fresh off winning the Mexican Open title in Acapulco, hammered five aces and broke de Minaur's serve five times.
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.
Federer, who defeated Federico Delbonis in the second round, will next face Jeremy Chardy after the world No 100 overcame countryman Adrian Mannarino, world No 23, 7-5 4-6 6-1.