Serrano, a freshman, came through with the Razorbacks' third final at-bat win this season after Dominic Ficociello and Matt Reynolds were intentionally walked with one out.
Jimmy Bosco led off the ninth with a single. Bo Bigham, pinch-running for Bosco, advanced to second on a Jacob Morris sacrifice bunt and to third on a wild pitch by SFA relief pitcher Hunter Dozier.
SFA (14-23) took a 3-2 lead in the top of the eighth on a Bobby Loveless fielder's choice, scoring Dozier, who reached with a leadoff double.
The run was charged to Mark Reyes, who left the game with one out in the eighth. Colby Suggs pitched 1 2/3 scoreless innings in relief to earn his third win for the Razorbacks.
Arkansas (27-10) swept the Tuesday doubleheader after winning the first game 8-3. The Razorbacks tied a season-high with 17 hits in the opener.
Ficociello, Bates and Gunn all had RBI hits in the first inning of the first game as Arkansas jumped to a quick 4-0 lead. Bates, who had last recorded a hit against Mississippi State on March 24, finished the first game 4-for-5 with 4 RBIs.
Bates had recorded 24 plate appearances without a hit prior to Tuesday.
Randall Fant pitched three scoreless innings to earn the win in the first game. Fant allowed only one hit and struck out four.
The Lumberjacks' only runs in the opener came on Loveless' three-run home run in the fourth inning off Arkansas reliever Chris Oliver. Loveless finished the doubleheader 3-for-7 at the plate with 4 RBIs.
The Razorbacks will travel to No. 22 Ole Miss for a three-game Southeastern Conference series beginning Friday.