After getting off to a fast start in the match, the second set began with a lengthy 15-minute service game for Raducanu, who lost her serve after saving four break points.
Stephens, who made the semi-final here in 2013 as a 19-year-old after defeating Serena Williams, started to find her groove as she cemented the break with her first service-hold of the match, but Raducanu stormed back to break at the next opportunity and level things at 2-2.
But the world No 67 had now settled into the match and won four games on the bounce to take the second set 6-2 and force a decider.
It marked Raducanu’s first-ever three-set match at Grand Slam level, having won all of her Wimbledon matches in straights as a wildcard last summer before retiring a set-and-a-break down in the round-of-16.