The Russian fifth seed battled in the second-round clash at Flushing Meadows on Wednesday, eventually claiming a 4-6 6-3 6-2 win over Romanian Dulgheru.
Sharapova made 46 unforced errors, including 22 in the first set, as she struggled to find rhythm.
The five-time grand slam champion said her experience meant she never felt in danger of an upset loss.
"Of course experience certainly helps, but she's a player that's been on the tour for many years. She has her fair share of experience as well," Sharapova said.
"But I felt that I was physically stronger today. No matter the conditions or the errors, being frustrated, I knew that in the end I was in better shape."
Sharapova said the conditions on Arthur Ashe Stadium, where she started during the day and finished under lights, were difficult.
"She [Dulgheru] played really well. Although I started off really good in the first couple of games, didn't take the opportunity to go up 3-0," she said.
"After that she started getting a little bit of a rhythm. It was difficult.
"Obviously the conditions were tough. You start in the sun; you finish under the lights. It was a very long match.
"Overall I felt like in the end I was in much better shape than she was and I could have played another few sets. Mentally that helped me a lot."
Awaiting Sharapova in the third round is 26th seed Sabine Lisicki, who powered past American Madison Brengle 6-4 6-1.
Despite holding a 5-1 win-loss record over the German, Sharapova said it would be tough.
"She's a great player. She's a very powerful, aggressive player. I expect a tough match from her," Sharapova said.