"He had a most unbelievable year where he won basically everything", Coric said.
"I have looked up to her all my life, she's a great player", said the teenager.
Sharapova is playing in her first Grand Slam tournament since serving a 15-month doping suspension.
"Both of us were looking forward to that match once the draw came out", she said. Bouchard dubbed Sharapova a "cheater" in one spring interview and leveled Sharapova, 7-5, 2-6, 6-4, on court when they squared with each other in Madrid. "Coming down from that and ending up on the winning side and knowing that there are many matches ahead of you, you just have to settle down".
"I think with the way that I played on Monday night, I don't think there are any more questions", said the 30-year-old, when pushed about whether her spot in the tournament was justified. Or maybe she just doesn't want to see that. "I keep letting people down", he said afterward.
"This girl has a lot of grit and she's not going anywhere", Sharapova told the crowd in an on-court interview.
In the men's part, Zverev, whose five ATP titles this year include a win over Roger Federer in this month's Montreal final, fell to 61st-ranked Croatian Borna Coric 3-6, 7-5, 7-6 (1), 7-6 (4).
Wembley is not the problem - Pochettino plays down curse after Burnley draw
They looked on course to win through not the prettiest of goals in not the prettiest of matches. But Pochettino insisted: " Wembley wasn't the problem".
After a slow start, Sharapova found her groove, brought her superior competitive instincts to bear, again showed off improved movement, and closed out another three-set win 6-7 (4), 6-4, 6-1.
Snubbed by the French Open and then injured for Wimbledon, where she would have had to fight her way through qualifying, Sharapova was controversially given a wild card in NY.
Any momentum Sharapova generated from that victory faded quickly as she dropped two of her first three service games and trailed 3-5 early on in the first set. As Sharapova stepped onto Arthur Ashe Stadium she mirrored Princess Diana circa 1994, when the royal wore a black Christina Stambolian "revenge dress" to upstage Charles and Camilla's affair.
Sharapova was also quizzed on her fitness after two slogs with Simona Halep and Babos on the back of an injury-hit year, amid suspicions she could go all the way in NY.
She already has spent almost five hours on court, and so perhaps the yelling and fist-pumping she showed at the end against Babos were as much a reflection of a sense of relief as celebration.
Sharapova did not play almost as freely as she had against Halep, when the pressure was largely on her opponent, but her famous fighting spirit was in evidence as she battled to a 6-7 (4/7) 6-4 6-1 victory.
The five-time Grand Slam champion will take on the American wild card Sofia Kenin in her third-round match.