"For me it felt like the first match I ever played on the Tour", said Djokovic.
"I feel like when you do come back from injury or when you haven't played in a long time, it just takes extra effort".
Resuming play beneath a pristine sky this afternoon, Federer hit a double fault at 5-all in the tie break to give Delbonis a set point.
But it was only a brief reprieve for Krajinovic, as the world number one romped into the next round in emphatic fashion.
It was another snag in the return for the 30-year-old Djokovic who admitted he was out of sorts while playing in just his second event of 2018.
On the men's side, Borna Coric of Croatia upset No. 13 Roberto Bautista Agut of Spain 6-1, 6-3; Jeremy Chardy beat No. 20 Adrian Mannarino 7-5, 4-6, 6-1 in an all-French matchup; and No. 11 Pablo Carreno Busta of Spain defeated Daniil Medvedev of Russian Federation 6-1, 7-5.
Play and win up to ₹40,000! "He's only going to get better from here", concluded the world number one.
Federer told reporters on Thursday that he won't be taking anyone for granted in this draw. Djokovic missed the last five months of the previous campaign to recover from his injury, but was unable to get back to his best despite months of rehabilitation.
"I was playing aggressive and feeling like he was not loving my slice", said Federer, who owns the No. 1 ranking.
In the evening session, seed Juan Martin del Potro dominates Australian teen De Minaur 6-2, 6-1.
With his triumph on Monday, Federer, victor of the 2018 Australian Open (20th Grand Slam title) and the Rotterdam tournament, extends his winning streak this year to 14-0.
For Daniel, this counts as the biggest win of his career and takes him into a third round meeting with Argentina's Leonardo Mayer, who defeated lucky loser Ruben Bemelmans, a late replacement for Kei Nishikori (withdrew with an illness) on Sunday. Wolrd No 5 Alexander Zverev slumped to a shock 7-5, 5-7, 6-4 defeat to unheralded Joao Sousa in his opening match.
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.
The French seventh seed beat the Australian 7-5 6-4 in just under two hours.