"It is very special for me", said the 23-year-old Svitolina, after reaching the last 16 at the Australian Open for the first time.
"I think I deserved to smile out there after that victory".
Stan Wawrinka, the 2014 Australian Open champion, No. 7 David Goffin and No. 13 Sam Querrey didn't make it through the second round.
Zverev, fancied as an outsider for glory in Melbourne, was frustrated by a lack of light as he was sent packing by NextGen Finals champion Chung in five sets.
She carried that form into her first-round clash with fellow German Anna-Lena Friedsam, winning 6-0 6-4.
Despite the convincing scoreline Djokovic was not at his best and was often frustrated on court.
The mouth-watering match-up of the only the two Australian Open winners - and Grand Slam champions - left in the women's draw got top billing on Rod Laver Arena but was turned into a tennis exhibition by Kerber.
With night matches generally reserved for the higher seeded players, Spaniard Rafael Nadal defended the scheduling following his straight sets third-round win.More news: One gunman killed, three remain inside Intercontinental Hotel in Afghan capital
In what was expected to be a tight affair, Del Potro (12) disappointed in a 6-3 6-3 6-2 loss to Tomas Berdych (19). "I think I have a small heat stroke for 40 minutes", said Monfils, who is considered one of the fittest players on tour.
The Swiss defending champion headlines Rod Laver Arena in the evening, with the 19-time Grand Slam victor tackling France's Richard Gasquet.
Sharapova finally got on the board, but flawless Kerber was finding winners nearly at will and broke again to take a 4-1 advantage in just 23 minutes.
Wawrinka also failed to progress, clearly still struggling from a lengthy knee injury lay-off in his straight sets defeat by American Tennys Sandgren. I've played a long match against Gael a few days ago. Garcia will play Madison Keys in the fourth round.
Now seeded 14th, Djokovic needed four match points in an eight-minute last game before clinching the win against Monfils, who needed a medical timeout for heat stress and said he had trouble breathing.
Still, he was back on court to take the next two 6-3 6-3 and will now face Hyeon Chung, who beat Alex Zverev, in the fourth round.
Keys will next play the victor of Saturday's later match between Aliaksandra Sasnovich and eighth-seeded Caroline Garcia.