Elsewhere, 16-year-old Amanda Anisimova shocked Petra Kvitova, ending her 14-match win streak. The Israeli only qualified for the contest as a lucky loser, while Edmund―appearing in his first match since the Australian Open―was widely backed as a dark horse to go deep into the tournament.
"I actually was explosive out there today and I felt good", he said.
Federer served six aces and broke the Krajinovic serve five times.
But Verdasco struck when it mattered, taking a 5-3 lead in the deciding set after breaking the Bulgarian and securing the match on the second match-point.
He said playing matches three days in a row doesn't faze him. Daniel plays next Argentinean tennis player Leonardo Mayer.
"I was grateful to be out on the court after surgery that quickly".
"At the Masters 1000s, when the format was different, it was the best-of-five-set finals in the finals".
Japan's Kei Nishikori withdrew through illness before playing his opening match of the tournament.
The 36-year-old had failed to win a Grand Slam title since 2012 when he chose to end his season after Wimbledon in July, 2016, which raised a number of questions about his future in the game.
The 36-year-old Swiss will face Frenchman Jeremy Chardy next after he beat Adrian Mannarino 7-5 4-6 6-1.
Federer and 10th seed Djokovic both came into the tournament seeking to become the first six-time victor of the event.
Borna Coric of Croatia upset 13th seed Roberto Bautista Agut 6-1 6-3 and Spain's Pablo Carreno Busta defeated Daniil Medvedev 6-1 7-5.
South Korea's Hyeon Chung, who surpassed all expectations to reach the Australian Open semi-finals earlier this year, also advanced, taking almost three hours to overcome Dusan Lajovic 6-7 (11/9) 6-3 6-3.