The 39-year-old eased to a 6-3, 6-4, 6-2 win under the Centre Court roof to maintain his latest bid for a record-breaking 25th Grand Slam title and record-equalling eighth Wimbledon triumph.
The Serb will next face French 25th seed Arthur Rinderknech on Friday for a place in the second week.
"I like the terminology 'vintage', it brings back the best days and you feel very satisfied and joyful on the court when you're playing this way," said Djokovic after being asked if it was a "vintage" performance.
Djokovic is bidding to become the oldest player to win a men's Grand Slam singles title in the Open era, but does not think his age is holding him back.
"I try not to take these moments for granted playing on Centre Court of a childhood dream tournament," he said.
"I feel very privileged to be walking out on the court at age 30 plus and I don't think it's a cliche, I actually believe age is just a number, I think it's true."
Title favourite Jannik Sinner, in the same half of the draw as Djokovic, has shown signs of frailty in both his opening matches.
Djokovic struggled at times against Wu Yibing in the first round, but was at his clinical best as he romped to a 12th successive win over Tsitsipas, a former world number three now languishing at 87th in the ATP rankings.
He won 88 percent of points behind his first serve, saved all five break points he faced, smashed 33 winners and made just seven unforced errors.
If he can maintain that level, Djokovic will be a real contender to move clear of Margaret Court for the Grand Slam singles record, and tie Roger Federer for most men's Wimbledon crowns.
Djokovic, the seventh seed, served out his 104th match win at Wimbledon after recovering from 15-40 down, never giving Tsitsipas a sniff of a comeback.
Greek Tsitsipas is a shadow of the player who reached two Grand Slam finals, losing both to Djokovic, and has not reached the third round of a major since losing in the 2024 French Open quarter-finals to Carlos Alcaraz.
Djokovic broke once in each of the first two sets before unveiling his full range of shots in the third.
His jovial mood was summed up by an exchange with a ball-girl after the second set, when he asked her to cut a tag off his t-shirt before jokingly pretended she had cut his arm.
During his post-match interview, the beaming former world number one also challenged Rory McIlroy, who was watching on from the royal box, to a tennis match for the golf star's Masters green jacket.
Wimbledon 2026
Wimbledon is taking place from June 29th to July 12th at the All England Club in south-west London. With 128 players in the draw, it is the third of the four Grand Slams of the tennis season and the only one played on grass.
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