Omaha scored first, bringing a run in on two singles, a stolen base and BYU throwing error to lead 1-0 after two.
The Cougars scored in every inning after that, tying the game in the third on a Danica Acosta single, Lily Owens walk and Hailey Shuler single.
Hailey Morrow and Townsend went back-to-back in the fourth, launching solo shots to left and center field, respectively, to give BYU a 3-1 lead.
Morrow homered again in the fifth after an Ilove’a Brittingham single and Rita Tavita sacrifice bunt for a 5-1 Cougar advantage.
The Mavericks answered in the home half of the fifth with a two-run home run of their own, making it a 5-3 game.
Three straight singles in the top of the sixth from Owens, Shuler and Brittingham plated another run for BYU, and it led 6-3.
Omaha responded once more, retaking the lead in the bottom half with a grand slam, going in front, 7-6.
Late game heroics ensued for the Cougars as Townsend hit her second home run of the game after a Morrow walk to put BYU back in front. Kaiya Fabela hammered a solo shot later in the seventh, the first of her freshman season, and the Cougars took a 9-7 advantage to the final frame.
Omaha got a run back in the bottom of the seventh on consecutive doubles and a sacrifice fly, but a foul out and sliding catch by Brittingham in center help BYU squeeze out the slugfest win.
On Deck
The Cougars will hit the road again next week, resuming Big 12 play at No. 21/15 Oklahoma State in Stillwater for a three-game series beginning Thursday, Mar. 19 at 6 p.m. CT.