Garner's bases loaded single came after Florida tied the game with three runs in the top of the ninth inning with a two-out rally.
Alabama (28-5, 9-3 SEC) collected four straight one-out singles in the bottom of the ninth inning to claim its fourth last at-bat win of the 2002 season.
After Jeremy Brown grounded out to short to open the inning, Hearod, Brent Boyd, Allen Rice and Garner followed with singles off losing pitcher Kevin Coleman (0-2). Garner's base hit came against a drawn in infield with one out in the ninth and easily scored Hearod with the winning run.
"Our team fights hard and always finds a way to comeback, which is a great quality," Alabama head coach Jim Wells said. "Mix in some good pitching and better defense and I thought we played much better overall this series.
"All three of our starters did a good job this weekend. We stayed with our pitching plan and our right-handers kept the ball in and out. Sanders did that today. He spotted his fastball and had a good changeup. He had good command of all his pitches. I can't say enough about what he did today."
Florida (24-10, 6-6 SEC) tied the game with a two-out rally in the ninth. After UA starter Shane Sanders retired the first two batters in the final out, he could not record the final out for his first career complete game.
Pat Osborn singled with two outs and Matt Kiger drew a walk to chase Sanders from the game. The UA senior worked a career-high 8 2/3 innings and allowed three runs (2 ER) on six hits. He added five walks and six strikeouts, both career highs. Sanders' previous career high for innings pitched was 6 1/3 innings in an 8-3 win over Florida Atlantic (Mar. 3, 2002).
Pinch-hitter David Klebonis greeted UA reliever Taylor Tankersley with an RBI double off the glove of Peter Stonard in deep right field. Aaron Sobieraj followed with a two-run single, scoring Kiger and pinch-runner David Riordan. Aaron Shealy followed with a base hit, sending Sobieraj to third. Tankersley avoided further trouble when pinch-hitter Ben Harrison grounded out to Rice at third base to end the inning.
Alabama plated the winning run in the bottom of the ninth for its 26ht consecutive home win, dating back to May 1, 2001. The win was also Alabama's 11th straight win over Florida, dating back to the final game of the 1997 regular-season in Gainesville.
Tankerlsey (5-2) earned the win despite his second blown save in the ninth inning. He allowed one run on three hits in one-third of an inning.
The Crimson Tide has won six straight series over the Gators, including three straight sweeps. Since 1995, Alabama has posted a 20-3 record against Florida.
Alabama took a 5-2 lead in the eighth inning on Spencer Pennington's first career home run. Pennington's two-run home run into the teeth of the wind in right-center field is the first home run by an Alabama football player since Philip Doyle in 1991. Pennington is a quarterback on the Crimson Tide football and is splitting time between the two sports this spring.
Florida benefited from an unearned run in the top of the second inning to take a 1-0 lead. Second baseman Aaron Davidson reached on a one-out walk and was picked off first base by Sanders, but first baseman Zac Welch dropped the ball, allowing Davidson to be called safe. Jeff Corsaletti followed with a single to right field, sending Davidson to third base. Brian Rose's sacrifice fly to center scored Davidson with the 1-0 lead.
After stranding runner in scoring position in each of the first three innings, Alabama finally scratched home a run in the bottom of the fourth to tie the game at 1-1.
The inning began with a walk to Jeremy Brown followed by a double down the left field line by Hearod, his second two-base hit of the game. Brent Boyd reached on a fielder's choice as Brown was thrown out at home by third baseman Pat Osborn. Allen Rice singled through the right side of the infield to load the bases with one out. Travis Garner reached on a fielder's choice when he grounded to third base. Hearod scored an unearned from third base when Rose dropped Osborn's throw at the plate. Zac Welch struck out and Scott McClanahan flied out, leaving the bases loaded.
Florida also left the bases loaded in the top of the inning when Osborn flied out to right field, stranding all three base runners.
Alabama stranded 13 base runners on Sunday, while Florida left nine men on base.
The Crimson Tide took its first lead of the game with two runs in the bottom of the seventh inning to grab a 3-1 advantage. Zac Welch, who was mired in a 2-for-25 slump, led off with a single to left.
UF starter Keith Ramsey, who gave the Gators a third straight solid outing, was lifted for left-hander Jamie Goldfarb. Ramsey allowed three runs on seven hits in six-plus innings, adding one walk and three strikeouts.
Goldfarb struck out McClanahan, who fouled off a bunt attempt with two strikes. Pavkovich followed with a single to center and Stonard reached on a fielder's choice. Pavkovich was out at second and pinch-runner John Marhsall moved to third.
Marshall broke the 1-1 tie as he scored from third on a throwing error by Goldfarb on a failed pickoff attempt.. Stonard moved to second on the play. After Brown was intentionally walked, Hearod singled up the middle scoring Stonard to give Alabama a 3-1 lead. It was Hearod's third hit of the game.
Ryan Shealy's SEC-leading 13th home run cut the deficit to 3-2 in the eighth inning.
Alabama outhit Florida 16-10 in the final game of the series. Hearod matched his career high with four hits and scored the winning run. Rice added a career high three hits for Alabama. Pavkovich also added three hits, while Garner added two hits.
Shealy and Corsaletti had two hits each for the Gators, who averaged 12 runs and 16 hits per game entering the series, but managed only eight runs and 26 total hits in the three games at Alabama.
The Crimson Tide will return to action Wednesday night as they travel to Birmingham to face the UAB Blazers at Young Memorial Field. The game will begin at 7 p.m. Alabama will also be on the road next weekend at Kentucky for a three-game SEC series.