The 29-year-old Serbian swept into the third round by beating France's Adrian Mannarino 6-4, 6-3, 7-6 (5) under the closed retractable roof at Centre Court while play was suspended elsewhere at the All England Club in London because of rain.
Djokovic, the two-time defending champion, has the third-longest Grand Slam match streak in the history of men's tennis. The longest winning streak at majors for a man is 37 matches, set by Don Budge from 1937-38, followed by Rod Laver with 31 and now Djokovic with sole ownership of third place on the all-time list.
"I have to be very grateful to have the opportunity to make the history of the sport," Djokovic told reporters. "Knowing that I won 30 in a row, it's very pleasing. I want to keep on going. Let's see where it takes me.
"Every single record that I managed to achieve in the last couple of years is important. Every next one that I have a possibility to achieve is more motivation."
Djokovic hasn't lost a Grand Slam match since falling to Stan Wawrinka in the 2015 French Open final.
Djokovic overcame eight double-faults, including one to get broken while serving for the match at 5-4 in the third set.
In the tiebreaker, Djokovic moved out to a 5-2 lead after a pair of cross-court winners. Mannarino later played a soft drop shot and Djokovic raced forward and slipped, falling onto his back as he knocked the ball into the net. Djokovic was unhurt and closed out the match three points later.
Djokovic holds all four Grand Slam crowns at the same time and is attempting to join Budge as the second player in tennis history to win five straight majors. Budge won six successive titles between 1937 Wimbledon and the 1938 U.S. Championships.
Djokovic, the two-time defending champion, also is looking to complete a calendar Grand Slam, already having won the Australian and French Open in 2016. He is bidding for a 13th major championship overall.
No. 3 Roger Federer, the seven-time Wimbledon champion, beat British qualifier Marcus Willis 6-0, 6-3, 6-4 in a match played under the Centre Court roof.
Federer won the first seven games and was in control throughout the match. Willis, ranked 772nd, was the lowest-ranked qualifier to reach the second round at a Grand Slam since 1988.
"It was very refreshing to play against an opponent like this," Federer said. "I always knew it was going to be a completely different match than everything that I've played before here at Wimbledon."
Before play was stopped by rain on the outside courts, No. 10 Tomas Berdych of Czech Republic stopped Ivan Dodig Croatia 7-6 (5), 5-7, 6-1, 7-6 (2).
On the women's side, No. 3 seed Agnieszka Radwanska of Poland beat Kateryna Kozlova of Ukraine 6-2, 6-1 in just over an hour under the roof on Centre Court to move into the second round.
"A one-hour match is always good, especially with that weather," Radwanska said. "Now we're playing every day, so I'm just very happy with that win and ready for the next one."
The match was played in its entirety under the retractable roof after steady rain forced delays on all other courts.
"It's like an indoor tournament, sometimes," Radwanska said. "Have to kind of get used to that. Of course, it's a little bit different without the sun, without the wind. So it's a different game. But, well, it's good that we could play today."
Matches canceled included No. 2 seed Garbine Muguruza of Span, No. 4 seed Angelique Kerber of Germany, No. 5 seed Simona Halep of Romania, Americans Venus Williams (8) and Madison Keys (9), Span's Carla Suarez-Navarro (12), Australia's Samantha Stosur (14), Ukraine's Elina Svitolina (17), Italy's Sara Errani (20), Serbia's Jelena Jankovic (22), Netherlands' Kiki Bertens (26) and Russia's Darya Kasatkina (29).