Three-time champion Djokovic untroubled again as he brushes aside Adam Pavlasek on Court 1.
Wimbledon 2017: Federer and Djokovic win but Pliskova crashes out
Seven-time champion Roger Federer reached the Wimbledon third round for the 15th time on Thursday with a 7-6, 6-3, 6-2 win over Dusan Lajovic of Serbia.
Third seeded Federer will face Germany's Mischa Zverev for a place in the last 16.
"I struggled at the start and couldn't find my rhythm," said Federer who dropped his first service game to trail 2-0 to his 79th-ranked opponent. "But once I got rid of the nerves I played some inspired stuff after that."
Zverev defeated world No 1 Andy Murray at the Australian Open this year, but Federer has won both his meetings against the left-handed serve-and-volleyer this year, including on grass at Halle last month.
Wimbledon title favourite Karolina Pliskova crashed to a shock second round defeat against world No 108 Magdalena Rybarikova on Thursday.
Rybarikova battled back from a set down to win 3-6, 7-5, 6-2 on Centre Court, earning the Slovakian a last 32 clash with Ukraine's Lesia Tsurenko.
Pliskova reached the US Open last year and the French Open semi-finals last month, but the Czech world No 3 has a dismal record at Wimbledon and for the sixth successive year she failed to get past the second round.
American Bethanie Mattek-Sands suffered a sickening injury at Wimbledon and had to be taken from court on a stretcher.
The 32-year-old player's knee appeared to buckle under her as she slipped during her second-round match with Romanian Sorana Cirstea on Court 17.
In obvious distress, Mattek-Sands screamed out "Help me" as she lay on the turf in front of horrified spectators.
She was attended to by paramedics on court, with an ambulance ready to take her away.
Mattek-Sands had won the first set 6-4 and lost the second on a tie-break moments before the fall occurred
Earlier, Wimbledon's blazing afternoon sun caused coach Andre Agassi to seek cover but Novak Djokovic was untroubled again as he brushed aside Adam Pavlasek on Court 1.
Three-time former champion Djokovic's first-round match against Martin Klizan was cut short by the Slovakian's retirement early in the second set on Tuesday, and his second outing proved to be another brisk affair, a 6-2, 6-2, 6-1 win in one hour and 33 minutes.
Agassi emerged to watch the match without a hat, and had to improvise by draping what looked like a tracksuit top over his bald head to stave off the threat of sunburn. He sat in a box at courtside alongside a short-term addition to Djokovic's team, the former top-10 player Mario Ancic whose regular day job is as an investment banker on Wall Street.
Djokovic was taking on plenty of water during each short break between games as the heat prompted some in the crowd to raise umbrellas to deflect the sun rays.
But it was clear from the early stages that while the heat was an issue, 22-year-old Czech Pavlasek would not be troubling him unduly, with an immediate break in the opening game establishing a tone for the match that was never challenged.
In May, a downbeat Pavlasek had expressed such concern about the state of his game to Czech media that he said it might take a psychiatrist or psychologist to set him back on track.
His form on the second-tier Challenger Tour this year has been largely awful, so taking on the second seed on a main show court was inevitably too tall an order for the world No 136.
While Djokovic, 30, came to Wimbledon on the back of winning the Eastbourne title, Pavlasek came off a very different run-up, having taken part in a low-profile Challenger in Poprad, Slovakia where an exhibition match featured dogs as ball collectors.
He remains perhaps best known as a former boyfriend of Petra Kvitova, the two-time former Wimbledon champion, and followed her out of the championships. Kvitova lost in the second round of the women's singles on Wednesday evening.
Djokovic moves on to bigger challenges, and more serious tests of his form. A double fault from Pavlasek brought this contest to an end, rather aptly.
"It was a very warm day, very hot day," Djokovic told the BBC immediately after coming off court.
"It wasn't easy to play point after point in some long rallies. Midway in the second set we had some long games, but overall from the very beginning I managed to impose my own rhythm and play the game that I needed to play.
"I think I definitely will feel better as days go by. I have been in this particular situation before many times and will try to use the experience knowing what to do on a daily basis to get myself in the right shape, the right state of mind and hopefully the right performance."