The Rays are 8-18 over their past 26 games, including five wins in seven games against Houston. Tampa Bay took three of four in the weekend series.
"We won, that's the bottom line," Rays third baseman Evan Longoria said. "We've got a lot of work to do. We put ourselves in a pretty good hole, but I think that the belief on a daily basis is still we can come to the ballpark and win."
Keuchel allowed five runs and nine hits in an eight-inning complete game. It was his third complete game this season.
"We did some good things today against a tough pitcher," Longoria said.
Dexter Fowler put the Astros up 1-0 when he hit the first pitch of the game from Erik Bedard into the left-field seats. It was his ninth career leadoff homer and third this season.
Bedard, who was with Houston last season, gave up two runs and seven hits in 5 1/3 innings.
Rodriguez made it 5-2 on an eighth-inning sacrifice fly.
Houston took a 2-1 lead in the third on Jose Altuve's single. Jonathan Villar opened the inning with a double, was awarded a steal of third after a replay challenge resulted in an out call being overturned and scored on the hit by Altuve.
Altuve has 13 hits in his past 24 at-bats.
The Rays tied it at 1 in the bottom of the first on Longoria's single
Desmond Jennings was caught attempting to steal home with Longoria batting to end the third, a call that was confirmed by a replay review. After catcher Carlos Corporan threw the ball back to Keuchel, Jennings broke for the plate, but was tagged by Corporan after a return throw from Keuchel.
"I know he does some uncharacteristic stuff," Kuechel said. "I don't turn my back from the guy on third, so I caught him out of the corner of my eye and just tried to get the ball out as soon as possible."
"I still think Desmond was safe," Rays manager Joe Maddon said. "I think throughout this whole process, the think that's really standing out to me, I'm into replay, I still believe there needs to be a separate group of umpires that are just out there specifically for replay only. That I hope would be the next step in regards to getting this thing nailed down."
SS Carlos Correa, taken first overall in the 2012 draft by the Astros, left Saturday's game with Class A Lancaster with a right ankle injury, which occurred while sliding. He will go on the disabled list. "Carlos was examined last night at a local hospital in California," Astros general manager Jeff Luhnow said. "He will travel to Houston early this week to be evaluated further by the Astros medical staff before determining next steps." ... Rays RHP Alex Cobb (2-5) will go against Pirates RHP Edinson Volquez (4-6) in the opener of a three-game series Monday. ... The Astros are off Monday. ... Houston starts a three-game series Tuesday against Atlanta with RHP Scott Feldman (3-4) and Braves RHP Aaron Harang (5-6) the scheduled starters. ... Three-year old Ireland Nugent, who has been fitted with leg prosthetics after a lawnmower accident, threw the ceremonial first pitch.
Copyright by STATS LLC and The Associated Press
ST. PETERSBURG, FL - JUNE 22: Dallas Keuchel #60 of the Houston Astros pitches during the first inning of a game...
13,841 (40.6% full) - % is based on regular season capacity
Home Plate - Brian Knight, First Base - Seth Buckminster, Second Base - Fieldin Culbreth, Third Base - Manny Gonzalez
Dallas Keuchel has allowed a .069 hard-hit average against his slider this season in 89 plate appearances to end in the pitch, which is ninth among qualified starters in MLB. Evan Longoria has a .038 hard-hit average against sliders this season, which is ninth-lowest among qualified batters.
Dexter Fowler (HOU): HR (6); while he was 0-for-10 in his previous 3 games, Fowler entered the game hot since the start of June, hitting .343 with multiple hits in 9 of 18 games since June 3.