Pegula had looked as though she would roll through the match as she won the first five games but had to find another level after Alexandrova fought back, and the American clinched it with a superb backhand winner down the line.
Pegula will play in Sunday's championship match against either Amanda Anisimova or Sofia Kenin, who face each other in an all-American semi-final later on Saturday.
Pegula broke her opponent in the first game with a backhand winner before Alexandrova helped the American to another break in the third game with a double fault and a clumsy shot that sailed past the baseline.
They traded breaks in the fifth and sixth games before the 26th-ranked Russian improved her form across the board in the second set, as she broke Pegula with a fine forehand shot in the sixth game and again with a forehand winner on set point.
They traded breaks three times in the final set before Pegula forced her opponent into an error on break point with a perfectly placed backhand at the net in the 11th game.