And when he faced him in the 10th inning, he remembered that past success -- and added to it.
"I remember him from last year when I hit the home run against Tampa," Morneau said. "The guys were even reminding me of that before the game today. That gave me a little confidence against him."
Morneau hit a three-run homer against the lefty last season when Miller was with the Devil Rays.
Morneau, who has a career-high 11-game hitting streak, hit his 17th homer to left-center on the first pitch from Miller (0-2).
"It helped me think of the way he pitches me and I knew he pitched a lot of curves so I was kind of looking for that," Morneau said. "And I got one right off."
Miller said he also remembered facing him in the past, but didn't address the earlier home run.
"I guess that was their game plan to swing early," Miller said. "But give him credit, he drove the pitch that he was looking for."
Joe Nathan (5-0) struck out the side in the bottom half to finish the back-and-forth win for the Twins, who have won 10 of their last 11.
Twins manager Ron Gardenhire said he's been impressed with how his team has rebounded after struggling on a West Coast road trip earlier this month.
"It's all about just playing better," he said. "We really stunk it up that last trip but we came home and got back to playing better -- running around the bases and slapping the ball everywhere. You put that with strong pitching performances and you're going to win some games."
Luis Castillo put the Twins ahead 5-4 in the top of the ninth when he scored on a wild pitch by Brad Lidge. But Preston Wilson homered off Nathan with two outs in the bottom half to tie it.
The Twins trailed 4-1 before they pushed across three runs in the seventh. Pinch-hitter Terry Tiffee hit an RBI single to left, Castillo drove in a run with a groundout and Nick Punto doubled in a run to tie it.
"We're struggling," Astros manager Phil Garner said. "There's no question about it. We had several opportunities to get it done but we didn't do the job."
Houston starter Roy Oswalt allowed four runs and nine hits in eight innings. He struck out seven and walked three.
Chris Burke hit a solo homer in the first and Lance Berkman added a three-run drive in the third to help Houston build a 4-1 lead. It was the 19th homer of the season for Berkman, who has 16 RBI in the last 10 games.
Twins starter Brad Radke allowed six hits and four runs with two strikeouts in six innings. Radke had allowed two earned runs or less in each of his previous four starts.
Morneau, who leads the Twins in homers and RBI (57), said things are beginning to click for him.
"I got a little confidence going," he said. "I like the way I'm seeing the ball now and the way things are going."
- Craig Biggio's single in the fifth inning was the 2,867th hit of his career, moving him past Harold Baines for 39th on the career major league hits list.
- Radke started against the Astros in the first interleague game in team history. Houston won that game 8-1 in 1997 at the Astrodome.
- Radke has allowed 75 career home runs in the first inning and five this season.
- Minnesota has scored four or more runs in 12 straight games for the first time since 1995.
- Berkman has 63 RBI this season.