The Russian, back on the grand slam scene for the first time since she returned from a 15-month doping ban in April, beat Hungary's Timea Babos 6-7(4) 6-4 6-1 on Arthur Ashe Stadium despite playing below her best.
"The saying 'the heart of a champion' was invented for her," Wilander, who is at the U.S. as an analyst for Eurosport, said in a daily chat with Reuters.
"She does not have a mental meltdown, it's amazing. She keeps hanging in, hanging in even if she's not playing well and expectations are through the roof for the rest of the people.
"She could easily have let go in the second set but as soon as she turns the second set around it's over."
Sharapova saved two break points to hold for 3-3 in the second set and after that won nine of the 11 remaining games and Wilander said her drive was key to her success.
"It's not enough to be a good competitor. Good competitors, they want to win. But with her you have the feeling she needs to win," he said.
"Today was another typical Maria Sharapova performance. She's been like that throughout her career. The great champions are not always those who have won the most, the great champions become great champions when people have expectations.
"Great champions always deliver. What people come to see, they give it to them.
"They don't come to see Sharapova win, they come to see Sharapova because they know they're going to get their absolute best fight.
"She delivers every single time. That's talent. She's a rock star."
(Reporting by Julien Pretot; Editing by Greg Stutchbury)
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