CHICAGO -- It was arguably a defining game for Tampa Bay's Chris Archer on Tuesday.

The Rays' right-hander threw a season-high 116 pitches, allowed three runs and eight hits, and collected an RBI with his first career base hit as Tampa Bay held on for a 6-5 victory over the Chicago Cubs on Tuesday.

He also shut down a sixth-inning rally after the Cubs had two runners on with none out and then came up empty.

"We needed a good start from Arch today and he provided that on the mound and at the plate so that was a pretty special day for him," Tampa Bay manager Kevin Cash said. "We really like Arch battling through that sixth inning to find a way to get out after first and second with no outs. That's pretty telling, a big moment in his season for us."

Archer (7-5) worked six innings, walked three and struck out eight and has 139 strikeouts for the season, second in the American League.

Tim Beckham went 2-for-4 and ignited a five-run fourth inning with a two-run homer while Steven Souza Jr. also had two hits to help Archer to his third victory in his last four tries.

Chicago starter Jon Lester (5-5) allowed six runs (five earned) and nine hits while striking out six in five innings.

"I don't want to sound like I'm making excuses," Lester said. "It just seems like balls are just getting outside of guys' reach. As a starting staff, as a bullpen I feel like when we do make mistakes we pay for it. Whereas last year when we made mistakes, guys just popped them up."

The defending World Series champions claimed a 1-0 lead in the second after Ian Happ tripled to right with one out and scored on Jason Heyward's sharp single to right.

Happ's long drive went in and out of Souza's glove for his second three-base hit of the season. Heyward, back after a two-plus week stay on the disabled list, delivered his RBI grounder on a 1-2 pitch.

The Rays forced a 1-1 tie in the third as Evan Longoria's one-out sacrifice scored Souza from third after Souza reached on a bunt single, stole second and went to third on catcher Willson Contreras' throwing error.

Beckham started the big fourth inning with his blast to left-center that also scored Trevor Plouffe, who led off with a single. It was Beckham's 11th homer of the season.

Adeiny Hechavarria and Peter Bourjos reached base and Archer helped his own cause -- still with none out -- with his first major league hit to bring home Hechavarria from second for a 4-1 lead.

"That felt good," Archer said. "I talked with Cash before the game and he said if (first baseman Anthony) Rizzo's in your face and you feel comfortable, do it. I got fortunate that they had that super shift on and the ball trickled through."

Souza's double to center then drove in Bourjos and Archer to make it 6-1.

The Cubs hit Archer for two runs in the fifth.

John Jay advanced to third on a bunt single and a throwing error by Longoria with two out and scored on Kris Bryant's infield single. Bryant moved to second on a Rizzo walk and scored on Ben Zobrist's single to make it 6-3.

Chicago put two on with none out in the sixth inning before Archer struck out the next three batters.

"One swing of the bat could have tied the game and I'm very, very happy I got the opportunity to work through it," Archer said. "I want the ball in those situations and going forward I hope to have the opportunity to get through it again."

The Cubs scored twice in the ninth as Rizzo delivered a one-out single to right-center off closer Alex Colome, scoring Albert Almora Jr. from second and leaving runners at first and third.

Zobrist hit a fielder's choice that brought home Jay to trim the Rays lead to 6-5. Colome walked Happ but got Heyward to pop out to left to end the game and give Colome his 22nd save.

Jay and Contreras each had two hits for Chicago.

"I don't have the definitive answer," said Bryant, who went 1-for-4 and is batting .262. "It would be nice if start hitting and scoring more runs. Our pitchers have been great. It just feels like we're not clicking at the same time."

NOTES: 1B Logan Morrison seeks to become the first Tampa Bay player since Evan Longoria in 2008 to win the All-Star Game final vote. He would join DH Corey Dickerson, who won a starting spot in tallies announced Sunday. ... Tampa Bay has hit 129 home runs, second in the majors behind the Astros, and have 24 in their last 13 games. ... The Rays send out LHP Blake Snell (0-5, 5.36 ERA) against Cubs RHP John Lackey (5-9, 5.24) on Wednesday. ... The Cubs activated OF Jason Heyward off the 10-day disabled list and recalled LHP Jack Leathersich from Triple-A Iowa. Chicago also optioned INF Jeimer Candelario and RHP Felix Pena to Triple-A. ... Cubs 3B Kris Bryant is among the NL Final Vote candidates for next week's All-Star Game. He'd join RHP Wade Davis, named an All-Star by player vote.