Valverde, who has two home runs and six RBI in the first two games, capped a four-run, ninth inning with a three-run home run to left field off losing pitcher Jonathan Settle.
Settle, who earned his second save of the season on Saturday, allowed four runs and three hits in his first loss of the season.
"I don't think I've ever hit a game-winning home run," Valverde said. "It was a fastball, middle-in. The guys in the dugout were razzing me about being on pace to hit 60 home runs. They told me it's my time now."
It was the first walk-off home run for Alabama since Brent Boyd beat Auburn 6-5 on April 27, 2002.
Trailing 4-3 in the bottom of the ninth, Alabama (1-1) junior shortstop Greg Paiml (Hoover) opened the ninth inning as he reached on a throwing error by Settle to open the inning. Paiml was thrown out at second base on junior center fielder Emeel Salem's bunt attempt. Senior first baseman Matt Downs (Centreville) flied out to right field for the second out before the Tide put together three straight two-out hits.
Senior second baseman Evan Bush (Rainbow City) singled to left field to send Salem to third base. Junior Brandon Belcher (Ruston, La.) followed with a single to right field to score Salem with the tying run. Valverde then settled the score with his second home run of the season to win the game.
"We don't count on back-to-back-to-back hits," Alabama coach Jim Wells said. "That really bailed us out there. Valverde got a first pitch fast ball. He got a pitch and did not miss it. It's nice to have a little power."
The ninth inning rally spoiled an impressive outing by Wintrop starter Heath Rollins. The junior allowed three runs and three hits in seven innings, with three walks and 12 strikeouts. He left the game after throwing 130 pitches.
The comeback also made a winner out of freshman RHP Tommy Hunter (Indianapolis, Indiana) in his collegiate debut. Hunter worked 3 1/3 innings and allowed one run and four hits, with no walks and two strikeouts.
Alabama trailed 4-0 after in the bottom of the sixth inning before Salem drew and leadoff walk and scored on a throwing error by Winthrop catcher Alan Robbins to make it a 4-1 game. The Crimson Tide added two more runs in the seventh inning on a solo home run by sophomore Matt Bentley (Hazel Green), his first career home run. Paiml reached on a two-out error by shortstop Matt Repec and scored on Downs RBI single to left to make it a 4-3 game.
Winthrop built a 4-0 lead through five innings, including three runs in the sixth inning. Ben Ehrlich led off the sixth with single up the middle and moved to second on a sacrifice bunt by Tyler McBride. Chris Carrara laced two-out double to right-center to to give the Eagles a 2-0 lead and chase UA starter Bernard Robert.
Robert (New Iberia, La.) allowed three runs and seven hits in 5 2/3 innings with four walks and four strikeouts in his UA debut.
Rollins, who also served as the designated hitter, greeted Hunter with a base hit up the middle to score Cararra to give the Eagles a 3-0 lead. Repec followed with with a double to right-center to score Repec and give Winthrop a four-run lead.
The Eagles took 1-0 lead in the second inning, but the damage could have been a lot worse. Winthrop loaded the bases and scored its first run of the game when Ehrlich reached on an error by Bush. Robert then settled down and got the next two hitters on strikeouts before Carrara flied out to end the inning.
Winthrop (3-2) out hit Alabama 11-6 in the loss. The Eagles also made five errors, which led to five unearned runs. Alabama committed three errors.
Repec had three hits and one RBI to led the Winthrop offense. The rubber game of the three-game series will be played Monday at 1 p.m. at the Joe. Freshman Austin Graham will make his first career start on the mound for the Tide against sophomore RHP Josh McDonald, a transfer from South Caroilina.
*Alabama used three more first-time players in Sunday's win over Winthrop. True freshman Ryan Rhoden (Tuscaloosa) made his first start in right field and Robert made his Crimson Tide debut on the mound.
*Hunter, another true freshman, made his collegiate debut out of the bullpen and earned the win in his Crimson Tide debut. Hunter allowed one run and four hits in 3 1/3 innings, with no walks and two strikeouts. He is the third member of the UA pitching staff to earn a win in his Crimson Tide debut, joining junior Allen Ponder (vs. Rice, 2003) and David Robertson (vs. Hawaii, 2005).
"Tommy Hunter was outstanding for the first time out as a college freshman," Alabama head coach Jim Wells said. "They bounced him around a little bit when he first came in, but they are a good team. He settled down, pitched well and did what we needed him to do."
*Sophomore Matt Bentley (Hazel Green) hit his first career home on Sunday, an opposiite field, solo blast to left field to lead off the seventh inning.
*Alabama and Winthrop combined for eight errors on Sunday afternoon.