The Rays improved to 7-9 this season. The Twins fell to 7-9.
Five different Tampa Bay players drove in runs, and Jason Hammel pitched six solid innings to earn his first victory of the season. Hammel threw 101 pitches, giving up three runs on six hits, while striking out five.
"He was making pitches, and he got threw some tough moments," Maddon said.
Hammel said he was trying to give his team a chance to win the game and earn a long-term spot in the Rays rotation.
"I kept the hitters off balance," Hammel said. "I made the pitches I needed to make. Right now I am pitching to win."
Hammel is 1-1 this season with an ERA of 4.26. In his last two starts, Hammel has given up five earned runs on 11 hits, while striking out 11 in 13 innings.
Nathan Haynes, who replaced Carlos Pena in the lineup midway through the game, notched two RBIs. With the bases loaded in the fifth, Haynes delivered an RBI single that brought home two Tampa Bay players.
"Huge hit in that situation," Maddon said about Haynes' production.
Pena was replaced after experiencing tightness in his right hamstring. Pena said he doesn't know how serious the injury is, but he will have it checked out on Friday.
"I felt some discomfort in the back of my knee, but I'm walking fine," he said.
Left-handed reliever J.P. Howell pitched three scoreless innings to close things out, earning his first career save.
"[Howell] has pitched well in situations," Maddon said. "He is very versatile."
An error by Denard Span led to Tampa Bay's first run of the game in the top of the first. Leadoff hitter Akinori Iwamura's blooper to right field handcuffed Span, allowing Iwamura to take second base. He then took third on a Carl Crawford grounder to second and scored on B.J. Upton's ground out.
Eric Hinske homered to right in the second inning to give Tampa Bay a 2-0 lead. It was the second straight game in which Hinske homered off the Twins, and was his fourth this season. The last time Hinske homered in consecutive days was in July of 2006 when he homered in three straight games.
A walk by Hammel in the third inning led to the Twins' first run after an RBI single from Matt Tolbert.
The two teams traded runs in the fourth inning. Tampa Bay's came on an Evan Longoria RBI single, while the Twins scored courtesy of a Delmon Young RBI single.
Tampa Bay collected 11 hits in the win. Haynes, Upton, Crawford, Hinske, Longoria and Jonny Gomes all had RBIs, and Crawford, Longoria and Jason Bartlett, each collected multiple hits.
The Rays return home Friday to face the Chicago White Sox.