The 12-time Major victor was beaten in the fourth round of the Australian Open in January after his elbow troubles had kept him out of action since the 2017 Wimbledon Championships.
The 36-year-old Swiss marvel continues to defy the ageing process, claiming his 20th Grand Slam title and sixth Australian Open crown in January.
'We wondered post surgery what it was going to look like, how his elbow was going to react to the strain and stress, but it was his heart and head that didn't react the right way in this match.
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.
"To me, it's not that surprising", Federer said of Novak's loss.
Federer returned to stadium court on Sunday afternoon and needed an hour to finish off his second round victory 6-3, 7-6 (8-6).
In other matches, 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.
"It feels insane. I mean, I'm still in shock", Anisimova said.
Frenchman Gael Monfils survived a match point before beating big-serving American John Isner 6-7 (5) 7-6 (3) 7-5 in a contest that had only one break. It is still early stages for Novak coming back and the first one after surgery.
"When you do come back from injury or when you haven't played in a long time, it just takes extra effort. Filip's wasn't so good and then things go quickly", Federer, who hit 24 winners, told Sky Sports in his on-court interview.
The tournament also lost Japan's Kei Nishikori, who withdrew through illness. So it was definitely nerve-wracking kind of, but I was enjoying it so much out there and I was playing my best. "I didn't serve too good today but overall I'm pleased".
Trump drops calls to raise guns age limit
The president and his fellow Republicans in Congress strongly support Americans' constitutional right to own guns. Senate Majority Leader Mitch McConnell, a Republican, has not scheduled debate for any gun-related bills.