Five Seattle pitchers combined on a five-hitter. The Mariners extended their scoreless streak to 19 games and won for the eighth time in nine games.
The Rays have lost 13 of 14 and are saddled with the worst record in the major leagues at 24-41. The last time they were 17 games under .500 was the end of 2007, the final year they were known as the Devil Rays.
Cano's big hit came during a three-run third inning against David Price (4-6), who struck out 10 in eight innings. The 2012 AL Cy Young Award winner has dropped three straight decisions and hasn't won in nine starts since beating Minnesota on April 22.
Mariners starter Erasmo Ramirez didn't allow a run, but failed to get through the fifth inning to qualify for the victory. The 24-year-old right-hander allowed four hits and walked five in 4 2/3 innings.
Joe Beimel (1-1) retired the only two batters he faced to get the victory, and Fernando Rodney worked a perfect ninth for his 18th save in 20 opportunities.
The Rays were shut out for the AL-high ninth time overall.
Seattle finished a 6-1 road trip. The Mariners won three straight over Tampa Bay after dropping the opener of the four-game series.
Price allowed three runs and seven hits and walked one. He has the best strikeout to walk ratio in baseball, but has also yielded a major league-leading 105 hits 99 2/3 innings.
Cano, who has an 18-game road hitting streak, delivered his two-run double after the Mariners loaded the bases on three singles. Stefen Romero had an RBI grounder that made it 3-0.
It was the majors-leading 41st time Tampa Bay has allowed three or more runs in an inning this season. Meanwhile, the Rays stranded seven runners and were 0 for 5 with men in scoring position through four innings against Ramirez, who entered the game with a 6.82 ERA.
The frustration continued in the fifth, when Ramirez gave up a two-out double to James Loney and walked Ben Zobrist before Mariners manager Lloyd McClendon turned to his bullpen.
Beimel fanned pinch-hitter Jerry Sands, ending the threat and eliciting smattering of groans and boos from the crowd of 10,400 at Tropicana Field.
NOTES: Struggling Grant Balfour is out as the Rays' closer. Manager Joe Maddon said the team instead will close games by committee. ... Mariners 1B Justin Smoak (sore left leg) and OF Michael Saunders (sore right shoulder) were out of the starting lineup for the third consecutive game. ... Rays rookie right-hander Jake Odorizzi (2-6) will go against St. Louis ace Adam Wainwright (8-3) in the opener of a two-game interleague series Tuesday night. Odorizzi grew up 35 minutes from St. Louis and called his start against the Cardinals a "special occasion." ... In a matchup of former teammates with Rakuten of Japan's Pacific League, Mariners RHP Hisashi Iwakuma (4-2) and Yankees RHP Masahiro Tanaka (9-1) will start in the opener of a three-game series in Seattle.