"That was a good, tough, hard-fought win and a great sign for us," manager Eric Wedge told reporters.
Bob Howry (2-1) worked two hitless innings and Bob Wickman got his seventh save with a typical high-wire act in the bottom of the ninth.
Wickman struck out Nick Punto, but yielded consecutive singles to Joe Mauer and Justin Morneau. Torii Hunter then popped out, but Jacque Jones drew a walk to load the bases for Lew Ford, who lined an 0-2 pitch to shortstop Alex Cora, who flipped to second base to force Jones and end the game.
Bard's homer was his first since Sept. 23, also against the Twins. The switch-hitting catcher entered the game just 1-for-13 this season, but went 2-for-4. His homer off J.C. Romero broke a 4-4 tie.
"Obviously, Bardo had a big hit for us," said Wedge. "He's the type of guy who keeps his head in the game and stays prepared."
Cleveland starter Kevin Millwood (4.34 ERA) battled through five innings. He gave up 11 hits and four runs, walking one and striking out six as he remained winless since signing as a free agent with the Indians.
"That was quite a start for Millwood," said Wedge. "He had to work hard and got through five innings. He gave us a chance to win. He's got mental toughness and bows his neck when he needs to. He's a competitor."
Morneau hit his fourth homer to help the Twins go ahead, 4-1. Blake singled home the Indians' first run in the second inning and hit his fifth homer, a two-run shot in the fourth to make it 4-3. Grady Sizemore tied it with an RBI double in the sixth. Sizemore (.262) went 3-for-4 off Twins starter Carlos Silva and is hitting .900 (9-for-10) in his career against the right-hander.
Travis Hafner (.306) went 2-for-4 and Aaron Boone (.122) ended an 0-for-17 slump with a swinging bunt that went for a fifth-inning single.
CLASS AAA BUFFALO (12-13) was blasted by visiting Scranton Wilkes-Barre, 12-1. Jeremy Guthrie (1-4, 9.78 ERA) gave up five hits, three walks and seven runs (four earned) over just 1 2/3 innings. Kaz Tadano (2.22 ERA) gave up one run and two hits over four innings, Matt Miller (3.86 ERA) and Chad Zerbe (4.60 ERA) finished. John Rodriguez drove in Buffalo's run with a sacrifice fly as the Bisons totaled only five hits.
CLASS A AKRON (15-9) split a doubleheader in Binghamton, winning the second game in extra innings, 4-3. Left-fielder Jason Cooper went a combined 4-for-7 in the two games to raise his average to .202.
The Aeros were hitless in the nightcap before Cooper singled to start the seventh inning. Jon Van Every (.206) beat out a bunt for a single and J.J. Sherill (.194) sacrificed both runners over. Pinch-hitter Anthony Lunetta (.286) was intentionally walked to load the bases and pinch-hitter Michael Aubrey (.294) followed with an RBI single to tie it 1-1 -- though Van Every was thrown out trying to score. Akron took a 4-1 lead with a three-run eighth that included two walks, a passed ball, sacrifice fly and an RBI single by Armando Camacaro (.185). Travis Thompson (2-0, 1.74 ERA) gave up two runs in the bottom of the eighth, but held on for the win. Aeros starter Brian Slocum (2.38 ERA) allowed one run and only two hits over six innings. He walked three and struck out six.
Cooper went 2-for-3 and hit his third homer as the Aeros got only four hits in a 3-1 loss in the first game. Lefty Billy Traber (0-1, 3.60 ERA) allowed six hits and three runs (two earned) over five innings in his first start since being promoted from Kinston. Chris Cooper (3.97 ERA) worked one scoreless inning.
CLASS A KINSTON (15-10) won in Lynchburg, 9-3, as third baseman Kevin Kouzmanoff (.363) went 4-for-5 with two RBI. Shaun Larkin (.293) went 3-for-5, Brad Snyder (.333) 2-for-5 with two runs, Ricardo Rojas (.161) 2-for-5 with one run and two RBI, and Caleb Brock (.207) 2-for-5 with one run and one RBI. Ron Bay (2-1, 2.42 ERA) struck out seven over six scoreless innings, allowing four hits and two walks. Mariano Gomez (9.00 ERA with Kinston), sent down recently from Akron, continued to struggle as he yielded three runs and five hits over two innings. Jim Ed Warden (11.57) pitched one scoreless inning.
CLASS A LAKE COUNTY (15-11) routed visiting Kannapolis, 13-3, as center-fielder Argenis Reyes drove in six runs. Reyes (.359) hit a grand slam in the third inning for his first homer of the season and went 2-for-4. Three other Captains had two hits and two RBI: Matt Whitney (.217), Chris Gimenez (.205) and Fernando Pacheco (.279). Right-fielder Chad Longworth (.241) went 2-for-4 and scored twice, while Brian Finegan (.239) and Jose Constanza (.235) both went 0-for-3 and scored twice. Aaron Laffey (2-0, 1.63 ERA) gave up two runs and seven hits over six innings. Michael Hernandez (1.12 ERA) allowed an unearned run over 1 1/3 innings and Scott Roehl (3.38 ERA) pitched a hitless ninth.