The 2017 US Open champion triumphed in two hours and 29 minutes, winning 4-6 6-3 6-2 in Guadalajara.
Stephens, who will play Russian Anna Kalinskaya in the last four, had not reached a hard court semi-final since the 2018 WTA Finals.
But the American was forced to do it the hard way after losing the first set, saving nine of 13 break points across the match, with her ability to win second serve points proving key.
Colombian Camila Osorio, the No.4 seed, was bundled out in 80 minutes by Kalinskaya 6-4 6-1.
There was also a straight-sets win for Marie Bouzkova after she defeated third seed Sara Sorribes Tormo 6-4 6-1.
She will face Wang Qiang in the last eight, who proved too good for Slovakian Anna Karolina Schmiedlova 6-2 6-3.
