Sunday's 2-6, 6-4, 7-6(9) win handed the Ukrainian wildcard a first win over Azarenka in a battle between the last two mums left standing out of the six who started in the singles draw as she snapped a five-match losing run against the Belarusian 19th seed.
After soaking up all the tension for close to three hours, world number 76 Svitolina finally toppled Azarenka with an ace on her second match point and promptly collapsed onto her back in her moment of triumph.
She will next face world number one Iga Swiatek (22) for a place in the semi-finals.
"It's really a shame that one of these players had to lose. They left it all on the court," nine-time Wimbledon champion Martina Navratilova concluded while commentating.
"In the end Svitolina played the braver tennis, particularly in the closing stages."
The Ukrainian summed up her achievement by saying: "After giving birth, this is the second happiest moment in my life."
Svitolina frustrated Azarenka for over 11 minutes in the fourth game of the match which dragged on for five deuces, with the Ukrainian missing a break point chance in the process.
Two games later the pair went toe-to-toe in a ferocious 25-shot baseline exchange that drew a chorus of 'oohs' and 'aahs' from the enthralled Court One crowd which only ended when Svitolina overcooked a forehand.
Even though the records will show the Belarusian romped through the first set by breaking twice, those in attendance will know that the scoreline failed to illustrate just how much drama was packed into those first 41 minutes of the contest.
TENSE ENCOUNTER
Since Russia's invasion of Ukraine, with Moscow using Belarus as a staging ground for what it calls a "special military operation", players from both countries have been blanked by Svitolina and her compatriots at tournaments.
That backdrop added another layer of tension to the match as the players faced off for the sixth time in their careers.
Azarenka may have thought she was on the home stretch when she opened up a 2-0 lead in the second set but two games later Svitolina finally punched a hole through her opponent's rock solid serve to break for the first time.
With the bludgeoning blows flying off Svitolina's racket thick and fast, Azarenka had to rely on her nerves of steel to fend off four break points in the eighth game that ebbed and flowed for over 11 electrifying minutes.
All the while it appeared that Svitolina had locked in to win the set and, after letting out an anguished cry when she missed her first set point by misfiring into the sky, she brought the hollering crowd to their feet by finishing off a 26-stroke rally with a thunderous forehand winner.
Seconds later she had levelled the contest after Azarenka swiped a forehand long to surrender her serve.
Svitolina, who returned to the tour in April following the birth of her daughter Skai last October, appeared to be on a roll when she opened up a 3-0 lead in the third.
But Azarenka kept her eyes on the ball and watched it bounce on the net three times in the fifth game before it trickled to her side of the net and she tapped it over to break back.
With both players refusing to blink, the contest headed for a match tiebreak won by Svitolina, who could not hold back the tears as she gave her war-ravaged homeland something to cheer.
"Back home there are lots of people watching and cheering for me and I know how much this means to them," she said.
While the crowd saluted Svitolina with a standing ovation, Azarenka was bemused as she left the court to a chorus of boos.
