In her first Grand Slam performance since winning the US Open, the young Briton triumphed over the American 6-0, 2-6, 6-1.
The 19-year-old stormed into a one-set lead, rattling off six straight games and dropping just four points.
But Stephens, who appeared rattled in the first, rallied in the second with some powerful ground strokes to even the contest.
After a brief setback, Raducanu started fast in the deciding set - a first-ever in her young career after failing to drop a set at Flushing Meadows last year.
And Stephens’ unforced errors piled up to ease the pressure on Raducanu, with the Briton serving out her victory in style.
“I think me and Sloane gave all we had, I thought it was a high-quality match, I'm very happy to come through against a champion like that,” Raducanu said after victory.
“It was a tough match-up for a first round, I'm very happy, I knew there'd be some long rallies. I had to work extremely hard, I'm so happy to have got through.
“I was very pleased, I thought I played some good tennis with few unforced errors, but then she was edging through with her defence.
“I don't think the score reflected the level, I was trying to get every single ball in, landing between the lines.”
Raducanu will now play Danka Kovinic, from Montenegro, in the second round on Thursday with the world No 99 beating South Korea’s Su Jeong Jang in three sets.
More to follow...