Lyons' eighth home run of the season, over the left-field fence, capped the highest-scoring inning of the season for the second-seeded Razorbacks.
Arkansas (35-22) entered the inning trailing 3-1. Ben Tschepikow led off the rally with a double and had two hits and two RBIs as Washington State's bullpen squandered a strong outing by Matt Way. Seven of the runs scored in the inning were unearned because of a throwing error by Washington State shortstop Shea Vucinich.
Andy Wilkins, who had a run-scoring single during the rally, went 3-for-5 with two RBIs as the Razorbacks posted their fourth win of the season over Washington State, which is making its first NCAA tournament appearance since 1990.
Way struck out 10 batters in six innings to break the Washington State season record for strikeouts set by former major leaguer Aaron Sele in 1990.
Jeremy Johnson took the loss for Washington State (31-24). Arkansas will play the winner of Friday night's Oklahoma-Wichita State game on Saturday night, while the Cougars will play the Oklahoma-Wichita State loser in an elimination game on Saturday afternoon.
Mike Bolsinger (5-4) earned the win for Arkansas, pitching two hitless innings to close the game in relief of starter Dallas Kuechel, who gave up three earned runs in seven innings. Reliever Jeremy Johnson (6-2) took the loss for the Cougars.
Greg Lagried had two RBIs for Washington State, including a seventh-inning sacrifice fly that put the Cougars ahead 3-1 before Arkansas mounted its rally. Vucinich went 2-for-5 and scored twice for Washington State.