Rodon yielded just one run, issued two walks and struck out eight in a dominating performance for the Wolfpack.
Logan Ratledge drove in two runs while Brett Williams and Bryan Adametz each rapped an RBI for North Carolina State, which used a four-run third inning to pull away from the heavily favored Tarheels.
The Wolfpack move on to Tuesday's winner's bracket, where they will play UCLA. The Bruins upended Louisiana State 2-1 in Sunday's late game.
The loss was hung on North Carolina's Kent Emanuel, who yielded five runs on six hits over 2 2/3 frames.
North Carolina will now play LSU in a Tuesday elimination game.
2014: The Year in Music [PHOTOS]