Defending champion Djokovic enjoyed a 6-4, 6-4, 6-4 win over Germany's Philipp Kohlschreiber with crucial breaks in the ninth game of each set.
But the world number one and top seed again found himself defending allegations that coach Boris Becker is using various means to coach him from the sidelines, a practice which is banned.
"I'm just trying to figure out what you want to achieve with this story. Do you want to say I'm cheating, my team? I'm really trying to figure out what's behind this," fumed the 28-year-old Djokovic.
The usually affable Serb added: "There are certain ways of communication which is encouragement, which is support, which is understanding the moment when to clap or say something that can lift my energy up, that can kind of motivate me to play a certain point. But it's all within the rules."
Djokovic, playing his first match since his defeat to Stan Wawrinka in the French Open final three weeks ago ended his hopes of completing a career Grand Slam, hit 12 aces and 36 winners past world number 33 Kohlschreiber. He next faces Finland's Jarkko Nieminen who defeated Hewitt 3-6, 6-3, 4-6, 6-0, 11-9 in a four-hour marathon.
Hewitt bids adieu
It was Hewitt's last singles match at the tournament - and 44th five-setter at the majors - as he plans to retire after next year's Australian Open. "To beat him here when it's my last time here as well, it's tough to find the words," Nieminen said.
Top seed Serena Williams, bidding to become the first woman since Steffi Graf in 1988 to wrap up all four majors in one season, endured a nervy start and was warned for swearing before completing a 6-4, 6-1 win over Margarita Gasparyan, the world number 113 from Russia who has never won a tour-level match in four years as a professional.
"It feels good so far. Just one match but it feels good just to be back here at Wimbledon. I've done so well here in the past so I'll always have so many good memories," said the 33-year-old American after her 73rd Wimbledon match win secured her a second round clash against Hungary's Timea Babos.
Fourth seed Sharapova also reached the second round with a 6-2, 6-2 win over Britain's Johanna Konta. Sharapova, the 2004 champion, will face Dutch qualifier Richel Hogenkamp for a place in the last 32.
"I was quite pleased with the way things went. It was my first competitive match in about four weeks, so I just wanted to start off really strong," said the Russian.
Venus cruises with 6-0, 6-0 victory
Five-time champion Venus Williams wasn't to be outdone as the 34-year-old American took just 42 minutes to crush compatriot Madison Brengle 6-0, 6-0.
Williams hit 29 winners to just two from Brengle, the world number 36. But hers wasn't the fastest win of the day as German 14th seed Andrea Petkovic needed just 38 minutes to see off Shelby Rogers of the United States.
Spanish ninth seed Carla Suarez Navarro went down 6-2, 6-0 to Latvia's Jelena Ostapenko in just 52 minutes while Italian 24th seed Flavia Pennetta lost 6-3, 2-6, 6-4 to Kazakhstan's Zarina Diyas.
Two-time semi-finalist Victoria Azarenka, seeded 23, saw off Estonia's Anett Kontaveit 6-2, 6-1 and seventh seed Ana Ivanovic breezed past Chinese qualifier Xu Yifan 6-1, 6-1.
37-year-old Haas wins
In the men's first round, Australia's 26th seed Nick Kyrgios, who knocked out Rafael Nadal last year, eased past Argentina's Diego Schwartzman 6-0, 6-2, 7-6 (8/6).
US Open champion Marin Cilic, the ninth seeded Croatian and a quarter-finalist at Wimbledon last year, got past Japanese qualifier Hiroki Moriya 6-3, 6-2, 7-6 (7/4).
Germany's Tommy Haas, at 37 years and 100 days old, and who first played Wimbledon in 1997, beat Serbia's Dusan Lajovic 6-2, 6-3, 4-6, 6-2 to become the oldest man to win a match at Wimbledon since Jimmy Connors (38 years 308 days) in 1991.
Japan's fifth seed Kei Nishikori needed his lower left leg strapped before clinching a gruelling 6-3, 6-7 (4/7), 6-2, 3-6, 6-3 win over Italy's Simone Bolelli. Meanwhile Canadian seventh seed Milos Raonic, a semi-finalist last year, beat Spain's Daniel Gimeno 6-2, 6-3, 3-6, 7-6 (7/4).