Both teams had other scoring opportunities with Sam Houston posting a narrow 12-11 advantage in shots.
Leask scored the match winner on a pass from Gabbi Coffee in the 65th minute. The Bearkats turned on the offensive pressure, firing five shots in the final 14 minutes.
Kayla Anderson had three of the final five shots with her best opportunity saved by Bobcat goalkeeper Lauren Frazer. Tricia Mallory led the Bearkat offense with four shots.
Sam Houston fell to 4-7-1 for the season while Texas State upped its season mark to 6-4.
The Bearkats continue their South Texas road trip Sunday afternoon at 1 p.m. when Sam Houston takes on UTSA in San Antonio.
The next home match for the Bearkats is Friday, October 7, when Sam Houston plays host to Northwestern State at Joseph Pritchett Field.