Cobb (8-2) did not allow a hit or a walk in 6.1 innings of work, before Pedro Alvarez broke up the gem with a bloop double down the leftfield line.
Tennessee loaded the bases in the bottom of the second with no outs and plated five runs in the inning. Cody Brown had a two-run single and Tony Delmonico chipped in with a RBI base hit to lead the way for the Volunteers.
UT added two more runs in the third to extend the lead to 7-0. They moved it to 9-0 in the fourth on Chris Kemp's solo homer and a RBI groundout.
Vanderbilt starter David Price (6-4) gave up nine runs, eight earned, on nine hits in 3.1 innings of work with three strikeouts and two walks in the losing effort.
Kemp hit his second solo homer of the game in the sixth to make it 10-0.
Pedro Alvarez scored the Commodores first run in the seventh and Dominic de la Osa scored on a fielding error by Julio Borbon to account for the two Vanderbilt runs.
J.P. Arencibia's RBI double in the seventh pushed the lead to 11-2.
David Macias added a sacrifice fly RBI in the eighth to make it 11-3. His 17-game hit streak ended, however, as he went 0-for-3 on the night.
The Vols closed out the scoring in the eighth with two more runs to push the score to 13-3.
The teams play the second game of the series tomorrow afternoon at 1 p.m. ET at Lindsey Nelson Stadium. Senior righthander Matt Buschmann is slated to throw for the Commodores, while sophomore southpaw James Adkins is scheduled to go for Tennessee.
Vanderbilt 000 000 210- 353 Tennessee 052 201 12x- (13)(14)2
Price, Zeid (4), Jacobson (8) and Hernandez, Hawkins. Cobb and Arencibia. W-Cobb 8-2, L- Price 6-4. SV- None. HR- VU: None. UT: Kemp 2 (10).