Edwards (5-0) held VU in check the entire game, limiting the team to just six hits while striking out three and walking three in MTSU's first complete game shutout since the 2001 season.
Middle Tennessee had 13 hits with Brentz, who came in hitting at a .448 clip with 13 homers, leading the offensive attack.
"Middle Tennessee is a very good team that is playing better than us right now," said Vanderbilt head coach Tim Corbin. "Bryce Brentz is a very good hitter, they scored in every inning but three and it was their night tonight. Edwards had good command and threw strikes and did a nice job with a complete game shutout."
Drew Fann, making a return to his hometown, led VU with two hits on the night.
The Blue Raiders took a 1-0 lead in the first when Tyler Burnett led off with a single and moved to third on a failed pick off attempt by starter Nick Christiani that went into right field. Bryce Brentz brought him home with a RBI single to center.
MTSU added two more runs in the fourth on Drew Robertson's single to center with runners on second and third with two outs.
Brentz continued his hot night with a two-run homer in the bottom of the fifth with two outs in the inning and then added a solo shot off of reliever Drew Hayes in the seventh to extend the lead to 6-0.
Christiani (3-2) allowed five runs, four earned, on seven hits in five innings of work with seven strikeouts and two walks in the losing effort.
The Commodores will be back in Southeastern Conference action this weekend as they travel to Arkansas to face the No. 1 Razorbacks in a three-game set. The first game is set for 6:35 p.m. on Friday, with a 3:05 p.m. start on Saturday and a 1:05 p.m. first pitch on Sunday.
Vanderbilt 000 000 000 - 064 Middle Tennessee 100 220 20x - 8(13)0Christiani, Hayes (6), Goodenow (8) and Giobbi. Edwards and Robertson. W- Edwards 5-0, L- Christiani 3-2. Sv- None. HR: Brentz 2 (15)