Mayers (5-3) struck out eight and allowed five hits and one walk for the Rebels (35-23).
Zach Kirksey was instrumental in both runs. He led off the fourth with his first triple of the season and scored on a groundout by Sikes Orvis. Kirksey drove in the second run with a sacrifice fly in the seventh.
Alex Yarbrough went 3 for 4 for Ole Miss. Brett Huber pitched the final two innings to earn his 10th save.
DJ Baxendale (7-4) allowed one run in six innings for the Razorbacks (39-19), who went 0-2 and produced only one run in the tournament. Brian Anderson had two hits.
Mississippi has allowed just two runs through two games, including Wednesday's 2-0 loss to Kentucky.
Rebels will play MSU-LSU loser at 9:30 a.m. Thursday.
Click here for more from Parrish Alford at the Inside Ole Miss Sports blog.
Read more in Thursday's NEMS Daily Journal newspaper.