Archer (4-3) gave up two runs and five hits in 7 2/3 innings and reached double digits in strikeouts for the fourth time in five May starts. Logan Morrison, Kevin Kiermaier and Steven Souza Jr. all went deep, and Alex Colome got four outs for his 13th save, winning a battle with slugger Miguel Sano with two on in the eighth inning.
Hector Santiago (4-3) gave up three runs and four hits and struck out six in 5 1/3 innings. Kennys Vargas and Brian Dozier drove in runs for first-place Minnesota, one of the surprise teams in the league this season.
Morrison and Kiermaier each hit two-run homers to put the Rays up 4-0 after six.
Routinely hitting 97 mph with his fastball and mixing in a knee-buckling slider, Archer set down 10 straight between an infield single from Jason Castro in the third inning and a sharp single from Joe Mauer in the seventh.
Vargas drove Mauer in to put the Twins on the board, ending the Rays' pitching staff's streak of scoreless innings at 23.
Archer now has 51 strikeouts in May and has one more start to break David Price's club record of 54 set in June 2014.
The Twins had life in the eighth with two on and two out and down three runs. But Colome got Sano to strike out for the fourth time in the game to escape the jam.
Rays: RHP Brad Boxberger, on the 60-day disabled list with a right flexor strain, is scheduled to throw a bullpen on Monday in Florida.
Twins: Closer Glen Perkins, who has been on the disabled list all season with shoulder problems, threw a bullpen on Friday. He will throw again on Tuesday before departing to Florida for extended spring training. ... Hard-throwing prospect Nick Burdi will undergo Tommy John surgery.
Archer got some help from his defense to put the clamps on a team with the fifth-best batting average in the American League.
Souza made a lunging catch at the wall in right field to take a hit away from Vargas in the second inning and Corey Dickerson sprinted to catch a liner from Mauer off of his shoelaces in the fourth inning.
Souza didn't have as much luck in the seventh inning, bizarrely diving for a ball struck by Vargas that landed at least 15 feet away from him. Souza shared a laugh with Kiermaier after both watched the replay.
When Souza stepped to the plate in the eighth inning, the Twins showed the replay of the dive on the video board. A good sport, Souza smiled as he stepped into the box, then belted a solo shot into the second deck in left field.
Rays: RHP Jake Odorizzi (3-2, 3.14) will start Game 2 on Saturday. Odorizzi leads the majors with 20 no-decisions since the start of last season, 16 of which have come after yielding two earned runs or fewer.
Twins: Molitor said that LHP Adalberto Mejia (1-1, 4.96) will be recalled from Triple-A Rochester to start Saturday's game. Mejia started for the Twins on Sunday, but was sent back down because Molitor has had to juggle the rotation due to so many rainouts early this season.
More AP baseball: https://apnews.com/tag/MLBbaseball