It was the third straight victory for the Red Sox, who entered the game with a 31/2-game lead over the second-place New York Yankees atop the AL East. Tampa Bay came in 31/2 games behind Minnesota for the second AL wild card spot.
Pomeranz (15-5) struck out seven, allowed two hits and walked two en route to tying Chris Sale for the team lead in victories.
Jesus Sucre slugged a two-run homer for the Rays, who have homered in a season franchise record 18 straight games.
Chris Archer (9-9) was roughed up for a season-high eight runs, six earned, and nine hits and struck out five in three-plus innings.
Betts hit his three-run homer off Pesky's Pole in right field in the first inning.
Boston chased Archer from the game with five runs in the fourth to build an 8-0 lead.
Pomeranz's no-hit bid was broken up by Brad Miller's one-out single in the fifth. Sucre added his two-run blast over the Green Monster in left field.
Both teams scored a run in the seventh.
Rays: RF Steven Souza Jr. left the game in the fourth inning after suffering a left knee bruise during a collision with the right-field wall. Initial tests revealed no structural damage and he will be re-evaluated Saturday. ... Former Yankee RHP Nathan Eovaldi (Tommy John surgery recovery) and LHP Xavier Cedeno (forearm) will pitch for Double A Montgomery in the Southern League playoffs Saturday.
Red Sox: INF/OF Eduardo Nunez experienced minor mid-back spasms during Wednesday's game and was out of the lineup. He is expected to return Saturday.... LHP David Price (left elbow inflammation) will throw two simulated innings of 15 to 18 pitches each on Saturday.
Tampa Bay's upcoming three-game series against the Yankees, scheduled to begin Monday at Tropicana Field in St. Petersburg, Florida, has been moved to Citi Field in New York because of Hurricane Irma.
"Wherever we need to play, we'll go play and hope for the best back home," Rays manager Kevin Cash said Friday.
JetBlue Park, the Red Sox's spring training home in Fort Myers, Florida, will serve as a headquarters for first responders during the storm.
Red Sox TV analyst Jerry Remy return to the booth to broadcast Friday's game after undergoing surgery and treatment for lung cancer. The 64-year-old was diagnosed with a fifth recurrence of the cancer and stepped aside in June.
Rays: RHP Matt Andriese (5-2, 3.78 ERA) hopes to replicate the success of his last start at Fenway Park on May 14, when he tossed five two-run innings. Andriese is 2-1 with a 4.11 ERA lifetime against Boston.
Red Sox: LHP Sale (15-7, 2.85 ERA) looks to break out of his recent funk after going 1-3 with a 5.48 ERA in his last four starts. Sale is 3-1 with a 2.48 ERA in four starts against Tampa Bay this season.