CLEVELAND -- Yandy Diaz had three hits and a run, and Drew Rasmussen carried a shutout into the sixth inning as the Tampa Bay Rays moved within one win of the World Series, beating the Cleveland Guardians 3-1 in Game 5 of the American League Championship Series on Sunday.

The teams had alternated wins for the first four contests before Tampa Bay claimed its second straight victory in Cleveland to seize a 3-2 lead. The Rays are seeking their third AL pennant and their first World Series title.

Game 6 is Monday in St. Petersburg, Fla., which would also be the location of Game 7 one night later. The National League champion Milwaukee Brewers await in the Fall Classic.

Rays ace Rasmussen (2-0) pitched seven innings, allowing one run on four hits to earn his first victory in seven career games in Cleveland. The right-hander struck out six and walked one, lowering his ERA in three postseason starts this fall to 1.29.

Cam Booser and Tyler Wells worked the eighth, and Bryan Baker pitched the ninth for his fifth save in as many postseason opportunities. The Rays tossed a combined five-hitter.

Jo Adell, Nathaniel Lowe and Travis Bazzana all came to the plate as the potential tying run against Baker, who walked Chase DeLauter to begin the ninth, but were each retired.

Tampa Bay's leadoff hitters scored in each of the first three innings against Parker Messick (0-3) and Tim Herrin, with Diaz, Ben Williamson and Chandler Simpson doing the honors in order to put the Rays up 3-0.

Messick walked Jonny DeLuca with the bases loaded in the first, bringing in Diaz, and Jonathan Aranda's single scored Williamson in the second. Liam Hicks had an RBI single off Herrin in the third.

Messick was chased after a career-low two innings, allowing two runs on five hits with a pair of walks. The left-hander struck out three over 57 pitches, the fewest in his 43 big-league starts.

The Guardians sliced their deficit to 3-1 in the sixth when Kwan singled and scored on DeLauter's groundout. Cleveland's only hit in the first five frames was a two-out single by DeLauter in the first.

Simpson, Aranda and Hicks had two hits apiece for Tampa Bay. Taylor Walls was thrown out at home by left fielder Kwan in the fourth.

Kwan singled twice and made a leaping catch at the center-field wall in the ninth, taking away an extra-base hit from Victor Mesa Jr.

Jose Ramirez reached base for the 17th straight postseason game, breaking the Cleveland franchise record. DeLauter tied the franchise record for hits in a single postseason by a rookie with 11.