The 10th-seeded Longhorns put together a nice finish to the third period and then hit enough free throws in the fourth to push past Western Grove 42-31.
Viola led 23-14 at halftime, but the Warriors refused to fold their tents and head home.
Instead, they managed to close the gap on the Horns in the third period.
Reeling off a 9-1 burst in the middle of the frame, including a big 3-pointer from Drew Baker, Western Grove edged within six points of Viola, 29-23.
But it turns out the Longhorns had an answer to Western Grove's challenge.
Dylan Holstine (11 points) pulled up off a fast break and drilled a 3-ball, followed by back-to-back buckets from Blake Baumunk (nine points) and Jackson Rains (four points) to restore order for Viola.
This 7-0 spurt edged Viola out in front 36-23 after three.
The Longhorns would not score from the field in the game's last eight minutes, but Marlin Coggins (seven points), Baumunk and Jacob Payne hit a pair of charity tosses apiece in the fourth to end Western Grove's bid for an upset.
Western Grove scored the first two baskets of the game to take an early lead, but that didn't last long.
Baumunk posted Viola's first hoop of the night with a layup and the Longhorns capped the first period with a hoop by Jordan Cotter and a triple from Holstine to take a 13-9 advantage after one.
Ethan Houghtaling (three points) started the second period with a bucket to keep Viola rolling and by the time Jesse Shrable ripped the nets for a 3-pointer late in the stanza, the Longhorns stood in front 23-14 at intermission.
And despite a charge from Western Grove after the half, Viola made its way to the second round of the tournament with an 11-point victory.
Matt Prinner finished with one point for Viola.