Two batters later, Fincher's single to left scored Jake Armstrong with the winning run.
"This team is pretty gritty," N.C. State coach Elliott Avent said. "This team is pretty tough. I'd pay money to come watch this team."
Christian Stringer had doubled in the go-ahead run for Rice, pulling a ball down the left-field line to score pinch-runner John Williamson. Hunter Kopycinski had three hits, including the one that put Williamson on base.
"We were set up like we wanted to be, and it just didn't work out for us," Stringer said.
Austin Kubitza of Rice and N.C. State's Carlos Rodon were locked in a duel for the first seven innings, with each starter allowing two runs before leaving the game. Rodon was removed in the ninth with runners on first and second, setting up Stringer's go-ahead RBI.
Rodon's streak of 26 2-3 innings without giving up an earned run was snapped in the fourth when an RBI single by Skyler Ewing cut the Wolfpack's lead to 2-1. Stringer tied it in the fifth with a solo home run to right field.
The Wolfpack scored two runs in the first when Trea Turner, who led off with a double, scored on a groundout, and Fincher came home on a wild pitch.
Kubitza gave up five hits and struck out eight before leaving in the eighth with runners on first and second. After a sacrifice bunt advanced the runners, Lemond retired the next two batters to escape the jam.
"It was such a tension-filled game," Avent said. "You've got two absolutely great college pitchers out there. We just knew it was awfully tough to score."
Rice had 11 hits against Rodon, the most the Wolfpack ace has allowed this season. Rodon struck out nine in 8 1-3 innings, the fifth straight start in which he worked at least eight.