Despite never playing a decider at a Grand Slam, it was the Bromley local who was first to strike in the third, breaking in the first game.
She prematurely went to over for the change of ends when going 40-15 up at 2-0, but eventually managed to serve out the game and sat down with a break-lead in the final set.
Mirroring her flawless first set, the Brit then raced to a 4-0 lead and managed to hold on in a lengthy, three-deuce game to extend her lead to 5-0 and put herself within a game of the match.
But it wasn’t to be another bagel, as Stephens got herself on the scoreboard one last time before Raducanu served out a 6-0 2-6 6-1 victory on her Australian Open debut.
It wasn’t without some drama as a ball boy needed to capture a bug on the court on match point, before the Brit hit a double fault and lost two successive points, finally converting her third match point
Raducanu will next face Danka Kovinic in the second round on Thursday.
The world No 99 defeated qualifier Jang Su-jeong in their opening match earlier in the day, winning 6-3 2-6 6-4.