Stephens will face Johanna Konta, the first British woman in the last-eight since 1983, for a place in the semi-finals.
The 26th seed had been a break down early in the first set but recovered and claimed victory on a fifth match point.
Stephens into second successive Roland Garros quarter-final
Highlights sloane stephens
Latest Videos
3:41 min
Ligue 1 Top 5 Goals: Matchday 38
4:22 min
Arsenal 5 Everton 1 - Highlights
0:35 min
Premier League Final Day - LIVE!
5:54 min
Report: Liverpool 3-1 Wolves
3:19 min
Highlights: LOSC Lille 2-2 Rennes
4:02 min
Highlights: RC Lens 2-2 Monaco
3:47 min