Kokkinakis had likened Djokovic to a "brick wall" before the match.
"It was one-way traffic. I got chopped today," said the 26-year-old Australian after his Centre Court torment.
Former world number one Murray, the 2013 and 2016 champion, went down 6-4, 7-6 (7/4), 6-7 (3/7), 6-4 to big-serving John Isner in his second-round clash.
Murray, now 52 in the rankings, failed to break serve once against 2018 semi-finalist Isner, who unleashed 36 aces and 82 winners in total.
"He didn't give me lots of chances," said Murray, whose previous earliest exits came in the third round in 2005 and 2021.
"My game was in a good place. I felt good on the court, just couldn't get the win."
Isner, 37, was gracious in the aftermath of his first win in nine meetings against the Briton.
"I am most definitely not a better tennis player than Andy Murray. I might have been a little bit better than him today," said the American.
Isner also took his career aces total to 13,724 to sit just four behind the record held by Ivo Karlovic.
Third seed and French Open runner-up Casper Ruud, who was scheduled to face Djokovic in the semi-finals, was knocked out by 112th-ranked Ugo Humbert, 3-6, 6-2, 7-5, 6-4.
But Spanish teenager Carlos Alcaraz stayed on course to meet the six-time champion in the last eight by reaching the third round for the first time.
Alcaraz, just 19, triumphed over Tallon Griekspoor of the Netherlands, 6-4, 7-6 (7/0), 6-3.
The flamboyant Spanish shot-maker goes on to face Germany's Oscar Otte for a place in the last 16.
Otte needed just 15 minutes to reach the third round when American opponent Christian Harrison retired injured at 3-1 down in their second-round tie.
Alcaraz's compatriot Alejandro Davidovich Fokina suffered a controversial exit at the hands of Jiri Vesely.
At match point down in the final set tie-break, Davidovich Fokina hit a ball out of the court, was penalised a point and lost the tie.
"I don't agree with it. That's crazy... what a lousy way to end it," US tennis great John McEnroe told ESPN.
In the women's tournament, second seed Anett Kontaveit, ninth seed and former champion Garbine Muguruza as well as 10th-seeded US Open winner Emma Raducanu all exited.
Kontaveit lost 6-4, 6-0 to Germany's Julie Niemeier as the Estonian endured another Grand Slam to forget.
Kontaveit has made the quarter-finals of a major just once in 29 attempts.
Muguruza, the 2017 champion, lost her delayed first-round clash 6-4, 6-0 to Belgium's Greet Minnen.
Raducanu, bidding to become Britain's first female champion at the All England Club in 45 years, was beaten 6-3, 6-3 by France's 55th-ranked Caroline Garcia.
"I really enjoyed playing on Centre Court, it was my first time and very special," said Garcia, who fired 25 winners past the British teenager.
There were no such dramas for third seed Ons Jabeur or fifth-seeded Maria Sakkari, who went through to the last 32 in straight sets.
Lesia Tsurenko came out on top in three sets over Ukrainian compatriot Anhelina Kalinina to make the third round for the second time.
Tsurenko, ranked at 101, proudly wore a ribbon in the colours of Ukraine on her shirt.
"It was a big court. Two Ukrainian players but a lot of people were watching us. We felt amazing support," said Tsurenko after her 3-6, 6-4, 6-3 win.
"Today on the way from hotel to the club, we got a driver," she added. "She has taken two people from Ukraine into her house.
"I think it's amazing when people help Ukrainians so much."