"It's an awesome team win," Hanigan said. "Top to bottom. Good pitching. Good defense. We all swung the bats pretty well."
Hanigan drove in his final two runs with a single off Yankees infielder Dean Anna, who gave up two runs and three hits in the eighth inning.
"When you see me in there, it's not a good day," said Anna, who last pitched when he was 11. "It was fun, but not fun at all."
Archer (2-1) allowed one run and three hits in 6 2/3 innings. He has won all four career starts against the Yankees, allowing four earned runs in 28 2/3 innings.
"I don't know," Archer said when asked about his success against New York. "My mentality is the same (every game). I just happen to throw really against them and execute pitches."
Yankees starter Ivan Nova (2-2) gave up a career-high four home runs before leaving in the fifth with right elbow soreness. The right-hander allowed eight runs and eight hits in four-plus innings.
"Obviously you're really concerned whenever a guy leaves a game because he feels something," Yankees manager Joe Girardi said.
Nova will undergo an MRI exam.
Myers hit his second homer of the game, a three-run shot off Matt Daley during a four-run fifth as the Rays took a 10-1 lead. The 2013 AL Rookie of the Year ended a 10-game RBI drought by driving in three runs in Tampa Bay's 11-5 victory Friday night over the Yankees in which the Rays trailed 4-0.
"I think yesterday was a big spark for us," Myers said.
Longoria hit his 164th homer, which broke a tie with Carlos Pena for the most in Rays history
"Longo is going to keep adding to that," Tampa Bay manager Joe Maddon said. "At least double that I think."
Myers put the Rays up 1-0 on his first homer since Sept. 16 in the second.
The Rays went ahead 4-0 in the third when Hanigan had a solo homer and Longoria added a two-run shot off Nova, who had his streak of not allowing more than one homer in a start end at 26. It was the first time Nova had given up multiple homers in a game since Aug. 21, 2012 when the Chicago White Sox hit a pair.
Hanigan extended the lead to 6-0 on his a two-run shot during the fourth.
Kelly Johnson hit an RBI double off Archer in the fifth.
Yankees right fielder Carlos Beltran went 0 for 3 as the designated hitter after sitting out Friday because of left shoulder and right wrist soreness. He flipped over the short wall down the right-field line while chasing Desmond Jennings' foul ball Thursday.
With a day game Sunday, Yankees SS Derek Jeter was rested. ... Longoria stopped a 49 at-bat homer drought. ... New York closer David Robertson (groin) threw 1 1/3 scoreless innings in an extended spring training game and expects to rejoin the team Tuesday. ... Yankees 1B Mark Teixeira (strained right leg muscle) went 2 for 4 in the same game as Robertson and said he is ready to return Sunday. ... Jennings was out of the lineup for the second straight game due to a groin injury. ... Tampa Bay recalled LHP C.J. Riefenhauser from Triple-A Durham. He threw 1 1/3 scoreless innings in his big league debut. ... Yankees LHP Vidal Nuno (0-0) and Rays LHP Cesar Ramos (0-1) are Sunday's scheduled starters.