Federer, playing the day's first match on Center Court, finished off a 6-1, 6-3, 6-2 win over Fabio Fognini before rain hit.
The rain caused a suspension of play across Wimbledon. Officials ordered the roof over Center Court closed and Djokovic, the last match on the court, was able to finish late and come away a 6-4, 6-4, 6-4 winner over Ryan Harrison.
Djokovic converted all three of his break chances -- one in each set -- and fought off the six Harrison had against him. Djokovic won 77 percent of the points on serve.
Federer needed just 74 minutes in dispatching Fognini. He had eight unforced errors and didn't have to deal with a break point. Federer won 80 percent of the points on serve.
Other second-round matches saw eighth-seeded Janko Tipsarevic handle Ryan Sweeting 5-7, 7-5, 6-4, 6-2, while No. 12 Nicolas Almagro beat Guillame Rufin 6-2, 5-7, 7-2, 6-4 and 15th-seeded Juan Monaco stopped Jeremy Chardy 6-2, 3-6, 6-3, 7-6 (9-7).
Other seeded players headed to the third round include 18th-seeded Richard Gasquet, 26th-seeed Mikhail Youzhny, 29th-seeded Julien Benneteau and No. 31 Florian Mayer. Unseeded second-round winners Wednesday were Denis Istomin, Jerzy Janowicz and Viktor Troicki.
In first-round play, from matches suspended Tuesday, seventh-seeded David Ferrer topped Dustin Brown 7-6 (7-5), 6-4, 6-4 without dropping serve while No. 21-seeded Milos Raonic defeated Santiago Giraldo 6-4, 6-4, 6-4. Jurgen Melzer ousted 25th-seeded Stanislas Wawrinka 3-6, 7-6 (7-2), 2-6, 6-4, 8-6.