Vanderbilt improved to 36-8 overall, while Tennessee Tech fell to 20-20.
Flaherty added a two-run double in the sixth to extend the lead to 9-4. Parker Hanks hit a pinch-hit two-run homer in the seventh to extend the lead to 11-4.
Tech plated six runs on six hits in the eighth inning to cut the lead to just one at 11-10. Scott Dunham and Michael Roeder had RBI singles, Cory Wright added a two-run double and Thomas Nelson chipped in with a RBI double to lead the way.
VU added an insurance run in the bottom of the eighth on a RBI groundout by Brian Harris to close out the scoring at 12-10.
Pedro Alvarez, Ryan Flaherty, Jonathan White and Ryan Davis each had three hits to lead the Vanderbilt 18 hit attack.
Justin Fields (1-2) was charged with the loss after giving up five runs on eight hits in four innings of work.
The Golden Eagles jumped out to a 2-0 lead in the first off of VU starter Brett Jacobson.
The Commodores got a run back in the bottom half on a RBI single by Dominic de la Osa.
Tech got the run back in the second on a solo homer by Michael Roeder in the second to make it 3-1.
Vandy cut it to 3-2 in the bottom half on a RBI single by Andrew Giobbi that scored Shea Robin who walked and stole second.
They tied it in the third on a RBI single by Pedro Alvarez that scored Dominic de la Osa that was hit by a pitch and stole second.
"I don't like the way the game started," said Vanderbilt head coach Tim Corbin. "I think defensively we had some miscues. I liked the way the middle of the game progressed where we hit the ball well and had some big homeruns. I thought Tyler Rhoden was pretty good. I liked his demeanor on the mound and it was good to see Ty Davis get out there and throw an effective inning. The ending, just one bad inning, that inning that makes the game looks like it just was completely out of hand and it wasn't."
The Commodores will close out their seven game homestand this weekend as Florida comes to town for a three games. The series begins Friday night at 7 p.m. and will continue on Saturday at 3 p.m. and Sunday at 1 p.m.
Tennessee Tech 210 100 060 -10(14)0 Vanderbilt 110 042 21x -12(18)1
Fields, Kearney (5), Edwards (6), Kilgore (7), Cole (8) and Soper. Jacobson, Rhoden (4), T. Davis (7), Zeid (8), Cunningham (8) and Robin, Hawkins. W- Rhoden 3-0, L- Fields 1-2. Sv-Crowell (2). HR- TT: Roeder (3) VU: de la Osa (11), Alvarez (13), White (3).