Rice broke open a 2-0 game in the fifth inning, scoring six runs to roll to a 10-3 victory against Charlotte on Saturday and clinch the series.
Eason went 2-for-2 with a single, double and three walks for the 49ers (4-4, 0-2 C-USA). Brad Elwood also had two hits.
J.D. Prochaska took his first loss of the year, giving up three runs on four hits while striking out five.
Rice improved to 10-6, 2-0.
North Carolina 6, Duke 2: J.B. Bukauskas threw six scoreless innings, scattering four hits and striking out eight for the host Tar Heels (10-3, 2-0 ACC).
Logan Warmoth added three hits and an RBI for North Carolina, which clinched the series.
Mike Rosenfeld had two hits and two RBIs to lead the Blue Devils (10-3, 0-2).
Duke starter Michael Matuella tossed three shutout innings, allowing one hit and one walk in the no-decision.
N.C. State 8, Clemson 3: Logan Ratledge hit two of the Wolfpack’s four home runs as N.C. State (8-4, 1-1 ACC) evened the series.
Curt Britt earned the win, pitching 5 1/3 effective innings in relief. Zack Erwin took the loss for the visiting Tigers (8-5, 1-1).
Weston Wilson hit a two-run homer in the fourth inning and Andrew Knizner added a solo homer in the seventh inning.
Yale 22, Davidson 3: The visiting Bulldogs rapped out 23 hits to improve to 1-1.
Clark Beeker took the loss for the Wildcats (5-4), giving up 13 runs on 14 hits and striking out five in 5 1/3 innings.
South Carolina 7, Miami (Ohio) 0: Jack Wynkoop scattered three hits over eight innings with five strikeouts for the host Gamecocks (11-3).
Connor Bright hit a grand slam for South Carolina.
The RedHawks fell to 2-7.
Winthrop 1, Maryland-Eastern Shore 0: Anthony Paulsen hit an RBI double in the sixth inning to lift the host Eagles (9-4).
Maryland-Eastern Shore is 2-9.
The Citadel 11, Elon 8: A late five-run push by The Citadel broke a 5-5 tie as the host Bulldogs (6-7) evened the series.
Casey Jones, Nick Zammarelli and James Ventuo each had two hits for the Phoenix (7-4).
Wofford 8, Gardner-Webb 5 (11): Alec Paradowski had three hits, while James Plaisted and Matt Pelt each had two RBIs for the visiting Terriers (11-4).
Collin Thacker had three hits and a pair of RBIs for the Runnin’ Bulldogs (10-4).
Valparaiso 17, USC Upstate 5: Nate Palace hit two home runs and had seven RBIs to even the series for the visiting Crusaders (3-7).
Tyler Jackson took the loss, giving up six runs on six hits for the Spartans (6-6).