Pennington, Bama's senior first baseman, had two hits and three RBI, including a game-clinching three-run home run in the Tide's five-run sixth inning that gave the Tide a seven-run lead.
Eighth-ranked Alabama Crimson Tide clinched a share of the Southeastern Conference Western Division championship and pulled within a game of SEC leader Kentucky with the win over UT at Lindsey Nelson Stadium.
The Crimson Tide stranded five base runners in the first three innings, and failed to score a run in the first third of the game, but in the end pounded out 11 runs on 18 hits.
The SEC Western Division title, at least a share of it, is the third for Alabama under head coach Jim Wells and first since 2002.
Georgia rallied from a 6-0 deficit against Kentucky, winning 10-9 to keep improve Alabama's (and Georgia's) hopes for an overall SEC regular season title.
With Thursday's win, Alabama can finish no worse than fourth in the SEC standings.
Tennessee (31-22, 11-16 SEC) is one game from being eliminated from SEC Tournament contention. LSU beat Florida 7-3 and now leads the Vols by 1 1/2 games with two to play. An LSU win or Tennessee loss will cinch a tournament berth for the Tigers.
Alabama roughed up UT starter Craig Cobb for a Tennessee single-game record 18 hits in the series opening win. Cobb (9-3) allowed 11 runs and 18 hits in seven innings, with one walk and four strikeouts.
Senior third baseman Matt Downs and senior catcher Kody Valverde had a career-high four hits each in the win. Downs was 4-for-5 with two runs scored and one RBI, while Valverde was 4-for-6 with two runs scored.
"I got myself in advantage counts and some fastballs to hit," Downs said. "I put some good swings on the ball tonight. This is a big start to the weekend. Hopefully, we can keep it going tomorrow."
Freshman right fielder Ryan Rhoden added three hits and two RBI in the win over the Vols.
Alabama and starter Bernard Robert survived a shaky first inning that saw Tennessee score two run on three pitches to grab a quick 2-0 lead.
Robert (7-5) settled down after the shaky first inning and held UT to one run and seven hits over the next seven innings to snap a personal three-game losing streak. Robert allowed three runs and nine hits in the win, with two walks and five strikeouts for his first win since April 9 at No. 1 South Carolina.