Djokovic handled Italian Potito Starace 7-6 (7-3), 6-3, 6-1, advancing to face Slovenian Blaz Kavic, who bested Lleyton Hewitt of Australia 7-6 (7-2), 6-3, 6-7 (4-7), 6-3 Monday.
Djokovic is seeking his initial French Open to title complete a career grand slam after wins last at the other three majors -- the Australian Open, U.S. Open and Wimbledon.
Federer, meanwhile, improved his career record to 233-35 in Grand Slam matches with his 6-2, 7-5, 6-3 win over German Tobias Kamke, tying Connors' mark of 233-49 -- most in the post-1968 Open Era.
The Swiss superstar lost to six-time champion Rafael Nadal in last year's finale.
Also on Day 2, 10-seeded American John Isner posted a 6-3, 6-4, 6-4 victory over Brazilian Rogerio Dutra Silva and No. 15 Feliciano Lopez of Spain withdrew while trailing France's Florent Serra 0-5 in the first set with a side muscle injury.
No. 20 Spaniard Marcel Granollers, 22nd-seeded Italian Andreas Seppi and No. 31 South African Kevin Anderson also logged victories Monday at Stade Roland Garros.