The Wolfpack (1-1) recovered from a 10-point deficit late in the first half to win their home opener.
The outcome ruined the return of Marshall coach Doc Holliday, a former N.C. State assistant coach. His team didn't score in the second half, and Marshall's hopes ended when a fourth-down pass was intercepted in the end zone by N.C. State linebacker Airius Moore with 1:34 to play.
Finley threw touchdown passes of 24 yards to Stephen Louis, 39 yards to Jaylen Samuels and 34 yards to Kelvin Harmon. Finley finished 29 of 36 for 341 yards.
Marshall receiver Tyre Brady set a stadium record in the 51-year-old facility with 248 receiving yards. The redshirt junior, who is a transfer from Miami, had 188 yards in the opening half.
Chase Litton threw for 350 yards on 26-of-43 passing for the Thundering Herd (1-1). He had a 1-yard touchdown pass to Willie Johnson and a 75-yard touchdown throw to Brady.
N.C. State's respected defense allowed 296 yards of total offense in the first half, but the Wolfpack went to the break holding a 23-20 lead.
The Wolfpack opened the second half with a 70-yard drive that took 13 plays and was capped by Reggie Gallaspy's 1-yard fourth-down run.
That was N.C. State's lone possession of the third quarter, with Marshall still with the ball to start the fourth quarter at the Wolfpack 29. The threat ended with Kaare Vedvik's missed 46-yard field goal attempt.
Gallaspy's 11-yard touchdown run with 3:58 left came on the first play after the Wolfpack recovered a fumble.
With N.C. State trailing 13-3, Louis slipped a would-be tackle and turned it into a 24-yard touchdown pass play with 5:26 left in the first half.
Then came Brady's catch-and-run that resulted in a 75-yard score and a 20-10 Marshall lead.
But a pair of touchdowns in a two-minute span late in the first half put N.C. State ahead for the first time since it was 3-0.
A flea flicker resulted in Samuels' touchdown play with 2:05 left in the first half as the Wolfpack closed within 20-17.
Following a Marshall punt, N.C. State drove 82 yards in seven plays with Harmon's touchdown catch at the 16-second mark.