Edenstrom scored in the 12th minute on a play that started with a Jessica Toms free kick. The boot by the freshman bounced off the cross bar and Edenstrom knocked the ball in for her second goal of the season to tie the score 1-1.
Rice tallied first on a header by Hayley Williams off a cornerkick in the 11th minute.
The Owls took control with a pair of goals with less than 20 minutes to play in the first half. Jessica Howard fired in a shot from close range in the 27th minute and Amy Berger scored two minutes later to put Rice up 3-1 at intermission.
The Owls picked up their final goal three minutes into the second half as Lauren LaFro scored off a deflection of a shot b Haley Williams.
Rice totaled 25 shots while the Bearkats had 10. Toms, Tricia Mallory and Kayla Anderson each accounted for two shots. The Owls goalkeeper was credited with four saves on SHSU shots.
Sam Houston dropped to 2-4 for the season with the loss while Rice upped its season mark to 4-1.
The Bearkats complete a five-match road swing with a trip to Denton to take on North Texas Friday at 7 p.m. The next home Sam Houston soccer match will be next Sunday against Texas Southern at 1 p.m. at Joseph Pritchett Field.