But fourth seed Federer broke back in the next game and seized the momentum when he blasted a cross-court forehand winner to break Krajinovic again and take the first set.
The Swiss coasted after that, thanks to an overpowering serve that Krajinovic struggled to read.
Federer, 37, said he had already put his loss to Dominic Thiem in the BNP Paribas Open final at Indian Wells last week behind him.
"Nowadays I am able to flush it out quickly. I was the worst at it when I was a teenager... right after it was all over I would cry and be so sad and disappointed," he said.
"I wasn't an angry person really, it just broke my heart.
"Nowadays I feel like 'look, I gave it all I had'. Thiem came up with the goods, I maybe didn't. That's it, it's over."
Next up for Federer is Russian Daniil Medvedev after the 13th seed defeated American qualifier Reilly Opelka 7-6(5) 6-7(5) 7-6(0) in a match that included 41 total aces.
Another big server, Anderson had 13 aces of his own with just one double-fault to seal a 6-4 7-6(6) victory over Portuguese Sousa earlier in the day.
The towering South African sixth seed, showing no ill-effects from the arm injury that hampered him earlier this year, will be a heavy favourite when he faces unseeded Australian Jordan Thompson, who beat Grigor Dimitrov 7-5 7-5.
Canadian teenager Denis Shapovalov dispatched 21-year-old Russian Andrey Rublev 6-3 7-6(5) in the pair's first career meeting as the sun set on a warm Florida evening.
Next up for Shapovalov is a mouthwatering clash with another fellow young gun, 20-year-old Stefanos Tsitsipas.
The Greek world number 10 was never broken on his way to a 6-4 6-4 win over Argentina's Leonardo Mayer in the night session.
American Frances Tiafoe battled back to defeat Spain's David Ferrer 5-7 6-3 6-3 to earn his spot in the fourth round, where he will face another defensive specialist, Belgian David Goffin.
(Reporting by Rory Carroll; Editing by Ken Ferris/Peter Rutherford)
