"The best game I've ever pitched in my life," Archer said.
Archer (4-3) struck out eight and walked none. He has nine starts this season after making his major league debut last year.
"The past couple games, I felt strong enough to continue to pitch deep into the ballgame, but really I've never pitched into the eighth inning before -- minor league, major league, little league, whatever," Archer said. "But they had faith in me to go deep. We scored enough runs so that there was no question. We played tremendous defense which saved me pitches, and I was able to execute."
Desmond Jennings homered as the Rays won for the 14th time in 16 games. Tampa Bay completed its most successful three-series homestand at 9-1, and went into the All-Star break in second place in the AL East.
Houston headed into the break with a 17-inning scoreless streak. The Astros have lost 12 of 15 and have the worst record in the majors at 33-61 during their first season in the American League.
Between Saturday's third inning and the fourth inning Sunday, the Astros went 11 straight innings without scoring or leaving a runner on base. Only four runners reached base in those 11 innings -- two were doubled up and two were picked off.
Jennings hit his 11th homer, connecting in the sixth off Paul Clemens after Kelly Johnson's third straight single. Jennings also preserved the shutout by running down Jason Castro's 400-foot line drive to center field for the final out with a runner on base.
"Archy deserved it," Jennings said. "He threw as well as he has all year. He deserved to finish that game. I thought from the fourth or fifth inning he was going to pitch the whole game, just by the way he was throwing every pitch where he wanted. That was fun to watch."
Archer turned in Tampa Bay's 15th consecutive quality start and went a second straight start without walking a batter. The Rays have won his last five starts.
"I think good can be an understatement," Houston manager Bo Porter said. "He was excellent today. It was more about him that it was about anything else."
Rays manager Joe Maddon agreed, and will have to determine whether Archer stays in the rotation when Alex Cobb comes off the disabled list.
"Archy's been on a roll, but to pitch a complete game shutout is different," Maddon said. "To go six innings and leave and get a win is a nice thing, but the complete-game shutout, when you teach yourself that lesson, the sky is the limit."
Jennings beat out an infield hit in the first and scored the first run on Evan Longoria's double.
The Rays added two more runs in the fourth with the help of a throwing error by Erik Bedard (3-6).
Bedard gave up eight hits and struck out six in five innings.
Cobb pitched off the Tropicana Field mound for the first time since being struck on the head by a line drive on June 15. Cobb called it "a relief" to be back on the mound and said he hopes to pitch in another game within a couple of weeks of the All-Star break. ... Longoria passed B.J. Upton and moved into second place on the Rays' career list for extra-base hits. Longoria has 341. Carl Crawford is the leader with 424. ... Rays SS Yunel Escobar left in the ninth inning with a mild hamstring strain. ... OF Chris Carter was out of the Astros' lineup for a second straight day due to a sore ankle. ... Astros LHP Brett Oberholtzer was optioned to Triple-A Oklahoma City after the game. ... Porter announced that Bud Norris will start the Astros' first game after the break Friday against Seattle.
Copyright by STATS LLC and The Associated Press
ST PETERSBURG, FL - JULY 14: : Pitcher Alex Cobb #53 of the Tampa Bay Rays throws some live batting practice...
21,180 (62.2% full) - % is based on regular season capacity
Home Plate - Will Little, First Base - Chad Fairchild, Second Base - Jeff Kellogg, Third Base - Eric Cooper
Chris Archer threw a shutout with 8 K and 0 BB and he's only 24 years old...
It's the 2nd such shutout by a pitcher younger than 25 this season within his first 15 career games (Shelby Miller on May 10)...
That had happened only twice in the previous 15 seasons (Zach Stewart in 2011 and Barry Zito in 2000)