The Serbian 24-times Grand Slam champion trailed Korda 5-2 in the second set but broke the American as he served at 5-3 and his precise and powerful serving carried him to the finish.
Aryna Sabalenka took a step closer to a first trophy of the year before her Australian Open title defence begins later this month.
Russian seventh seed Daniil Medvedev, the 2023 Miami champion who arrived this year fresh off a run to the Indian Wells semi-finals, crashed out at the first hurdle as he fell 6-2, 6-3 to Spaniard Jaume Munar.
Images from the quarter-final matches played at the Australian Open at Melbourne Park on Tuesday
Grigor Dimitrov dispatched American 10th seed Frances Tiafoe in straight sets with a convincing 6-2 6-3 6-2 victory on Sunday.
A relieved Rafael Nadal felt the confidence come flooding back in a first-round romp at the Australian Open on Monday.
Coric's positive test follows that of Grigor Dimitrov, who said on Sunday he had contracted the novel coronavirus.
Coco Gauff forgot to bring her rackets to the court but reminded her rivals of her French Open title ambitions with a commanding win while Daniil Medvedev lost his composure on a cold and blustery Tuesday as he crashed out in the opening round.
'I'm happy to be part of this Italian movement. People, they start to play tennis now more and more, which is great to see. I think that's the most important.'
Djokovic's father blamed the cancellation of the tour on Dimitrov. There is nothing to suggest that Dimitrov spread the virus to others.
Here's a peek at the stars who came out to cheer the tennis stars...
Sharapova was broken in the first game but fought back to draw level before going on to take the first set with a hold to love.
Madison Keys was dumped out of the Miami Open third round on Sunday, falling 6-4, 6-2 to Philippine wild card Alexandra Eala
The 29-year-old Spaniard, who needed a final-set tiebreak to fight past Lukas Rosol in the first round, produced a performance of defiant persistence to fend off the challenge of the 24-year-old Dimitrov.
Team Europe and Team World are tied at 2 after one day of the Laver Cup after play opened Friday in Berlin.
American Frances Tiafoe celebrated his 21st birthday by stunning Bulgaria's Grigor Dimitrov 7-5, 7-6(6), 6-7(1), 7-5 in the fourth round of the Australian Open on Sunday.
Top seed Andy Murray cruised past Spain's David Ferrer 6-2, 6-3 on Saturday and Bulgaria's Grigor Dimitrov received a walkover into the China Open final after Milos Raonic withdrew due to an ankle injury.
Spanish fourth seed Garbine Muguruza fine-tuned her preparations for this month's U.S. Open by crushing Simona Halep 6-1, 6-0 in the Cincinnati Open final on Sunday.
Top seed Rafa Nadal, who has won the tournament 10 times, also reached the last eight after dispatching compatriot Guillermo Garcia-Lopez 6-1, 6-3 and claiming a record-extending 40th consecutive set on clay.
Carlos Alcaraz failed to reach the Paris Masters quarter-finals after a thrilling 6-1, 3-6, 7-5 defeat to local favourite Ugo Humbert
IMAGES from the French Open quarter-finals played in Paris on Tuesday.
Djokovic saved three breakpoints in stifling conditions to go 5-4 up but lost the opening set in a tough tiebreak as Opelka cranked up his serve
Novak Djokovic and Nick Kyrgios enthralled fans on their debut as a doubles team on Monday
Roger Federer moved to within one win of his 1,000 career victory when he crushed Bulgaria's Grigor Dimitrov on Saturday to reach the final of the Brisbane International.
Defending champion Stefanos Tsitsipas showed no signs of fatigue following Friday's marathon battle as he eased past German Alexander Zverev 6-4, 6-2 to reach the Monte Carlo Masters final on Saturday.
Andy Murray knows time is no longer on his side as the 36-year-old conceded that another deep run at a major may not be within his reach after exiting the US Open on Thursday.
Grigor Dimitrov reached his first grand slam quarter-final in over two years on Monday by defeating an injury-hampered Denis Istomin 2-6, 7-6(2), 6-2, 6-1 to end the Uzbek wildcard's fairytale run at the Australian Open.
Protesters briefly interrupted play on the third day of Wimbledon, releasing orange ticker-tape mixed with jigsaw puzzle pieces on Court 18.
Carlos Alcaraz kept his Indian Wells 'three-peat' campaign on track with a straight sets win against Canadian Denis Shapovalov in the third round.
Last week the men's ATP and the WTA, which runs women's events, issued revised calendars for the resumption of the circuit from August while organisers of the US Open said the Grand Slam will be staged without fans as scheduled from August 31 to September 13 in New York.
Roger Federer celebrated his return to the top of the world rankings with his second title of the season, swatting aside Grigor Dimitrov 6-2, 6-2 in the final of the ABN AMRO World Tournament in Rotterdam on Sunday.
Djokovic has had to deal with suspicion about the severity of his hamstring injury, which he suffered en route to winning the warm-up title in Adelaide.
Defending champion Stanislas Wawrinka and compatriot Roger Federer suffered contrasting third round defeats at the Monte Carlo Masters on Thursday.
Tennis superstar Serena Williams has her daughter Alexis Olympia Ohanian literally walking in her footsteps.
Novak Djokovic marked his return to Serbia, after being stranded in the Spanish resort of Marbella for two months due to the coronavirus lockdown, by announcing that he has organised an event which will be contested across the Balkans. When the world number one had travelled to Marbella with his family in mid-March to visit his younger brother Marko, he had no idea it would be another two months before he could return to his homeland on Sunday.
Images from matches played on Day 7 at the Australian Open in Melbourne Park on Sunday
IMAGES from Day 7 of the Wimbledon Championships, at the All England Lawn Tennis and Croquet Club, London, on Sunday.
Images from Day 6 of the French Open matches played at Roland Garros in Paris on Friday.
Defending champion Rafael Nadal remains on course for an 11th Monte Carlo Masters title after beating Bulgaria's Grigor Dimitrov 6-4, 6-1 in the semi-finals on Saturday.
Medvedev whips Dimitrov to enter US Open final
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