"The team, we played our tail off. We battled," said Archer, who struck out 10 while holding the Tigers to a pair of singles in 5 2/3 scoreless innings. "It’s a tough one to lose because we really battled up until the end."
Justin Upton snapped a 1-1 tie with a two-run double and Kinsler’s 16th homer of the season gave Detroit’s bullpen a comfortable cushion to finish the sweep.
But it was Kinsler’s alert baserunning got the Tigers going after he began the Detroit eighth with a double off Matt Andriese (6-2). Victor Martinez kept the rally alive by hustling up the first base line to avoid grounding into what would have been an inning-ending double play that would have allowed the Rays to cling to a 1-0 lead.
Kinsler scored from second base on the play, tying the score.
"I do that every time I’m on second. When there’s an opportunity for a double play across the infield, that’s something I was taught — with two outs, you have an opportunity to score a run right there," Kinsler said.
"And obviously the play doesn’t happen if Victor is not busting his tail down that line and beating that throw," Kinsler added. "You’re just looking for opportunities to score, and on that play it worked out perfect."
With his two-run homer, Kinsler joined Carlos Beltran, Alex Rodriguez and Jimmy Rollins as the only active players with at least 200 home runs, 1,000 runs scored, 1,600 hits and 200 stolen bases.
Bruce Rondon (2-0) retired the only two batters he faced, bailing starter Mike Pelfrey out of a bases-loaded jam in the seventh to get the victory.
Archer, meanwhile, rebounded a slow start to pitch into the sixth. The AL strikeout leader allowed the first three batters to reach base before fanning Martinez, Castellanos and Upton to put down the threat.
"Can’t help but feel really good about what Chris Archer did. For the way it started and the way he kicked it into gear," Rays manager Kevin Cash said. "That was an outstanding effort, outstanding performance for him to even get remotely close to getting his pitch count back in order. You don’t foresee guys going that deep like he did."
Archer, who entered Sunday with a 10.06 ERA in the first inning compared to 3.65 in subsequent innings, boosted his season strikeout total to a league-leading 127.
"It’s frustrating, but definitely not something I dwell on," Archer said of his first-inning woes.
"It does alter the course of the game and makes the bullpen come in a little earlier than need be," he added. "I don’t beat myself up over it. You have to move forward, and you have to give a team your best after all the stuff happens. I think I did a decent job of that today."
Tigers: CF Cameron Maybin, who batted .591 (13 for 21) in six games against Tampa Bay this season, was out one day after a seven-game hitting streak ended. He entered the game as a pinch-runner.
Rays: CF Desmond Jennings (left hamstring tightness) was out of the lineup for the third straight game. . Closer Alex Colome (right biceps tendinitis) had a bullpen session. . INF Steve Pearce (strained right hamstring) hit in an indoor cage. . RHPs Chase Whitley (Tommy John surgery) and Brad Boxberger (left oblique) will throw to hitters on Wednesday.
RELIEF ON THE WAY?
The Rays concluded a stretch in which they played 20 consecutive games against teams with winning records, going 4-16. The last-place Angels arrive Monday for a four-game series that finishes an 11-game homestand. Tampa Bay has played more games (62) against opponents with a .500 or better mark than any other team.
Tigers: LHP Daniel Norris (1-0) will make his third start of the season Monday night at Cleveland. He allowed two runs and eight hits over five innings of a 10-3 victory over Miami last Wednesday.
Rays: LHP Matt Moore (4-5) faces the Los Angeles Angels for the first time since September 2013, when Tampa Bay begins a four-game series Monday. Moore is 3-0 with 1.52 ERA in four career starts against the Angels.