It was a familiar sight at Jacobs Field the bases loaded with Cleveland Indians and the game on the line but the ending Sunday was different than usual.
"Confidence, that was the key," Hernandez said after getting Thome on a called strike three to earn his 36th save and 15th in a row.
Baines, who had gotten two big hits for Cleveland since being acquired Friday from Baltimore, then lined to shortstop.
"The one ball hit hard in the inning and it was caught," Tampa Bay manager Larry Rothschild said. "Go figure baseball."
Alvarez (9-6) allowed three earned runs in eight innings. He struck out six and walked two in his sixth win in seven decisions since June 14.
It was the left-hander's fourt career win at Jacobs Field, most by an opponent since the ballpark opened in 1994.
"We had our chances," Indians manager Mike Hargrove said. "Had the bases loaded a couple of times and got nothing. When you do that you are just burning runs."
Ramirez drove in two runs, giving him 133 RBIs, most in the majors.
McGriff hit a two-run homer in the first and Jose Canseco had a two-run single in the fifth for the Devil Rays.
"It feels good to come through," Ledesma said. "It has been kind of a roller coaster ride for me this season, but a hit like that makes things a lot easier."
Tampa Bay made it 6-4 in the seventh when Canseco walked and scored all the way from first when Bubba Trammell singled to right and the ball was misplayed for an error by Ramirez.
Ramirez had a sacrifice fly in the first. The Indians tied it at 2 in the third when Einar Diaz drew a leadoff walk and scored as Roberto Alomar's two-out fly ball to right dropped near Guillen, who appeared to lose sight of it in the bright sun and was charged with an error.
The Indians went ahead 3-2 in the fourth when Richie Sexson tripled and Thome doubled.
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