Franklin had his first three hits of the season, and Logan Forsythe and Desmond Jennings also homered in support of rookie left-hander Blake Snell (1-2), who allowed four runs and eight hits over 5 1/3 innings to get his first big league win.
Tampa Bay's skid matched the longest in the majors this season. The 23-year-old Snell became the first AL rookie starter to stop a losing streak of 11 or more games since 2009, when David Price also stopped an 11-game skid for the Rays.
Forsythe finished with three of Tampa Bay's season-best 18 hits, including a two-run homer off Eduardo Rodriguez (1-3) that gave Snell a 9-0 lead in the third inning. Logan Morrison drove in two during a five-run first, and Jennings led off the third with a solo homer.
Rodriguez continued to struggle in his comeback from a stint of the disabled list (right patella subluxation), allowing nine runs and 11 hits in 2 2/3 innings.
Boston fans sprinkled throughout an announced crowd of 18,024 cheered sarcastically in the second, when the Red Sox finally had a reliever start warming in the bullpen after Franklin's RBI single increased Tampa Bay's lead to 7-0. Forsythe's homer ended the Boston starter's night, giving Snell a nine-run cushion -- though not necessarily an easy path to victory.
Bryce Brentz had a two-run double for Boston in the fourth, and the Red Sox loaded the bases with two outs in the fifth. Snell walked David Ortiz, forcing in a run but escaped further damage by striking out Hanley Ramirez. The young lefty yielded another run in the sixth, exiting after throwing 103 pitches.
Ortiz moved ahead of Hall of Famer Reggie Jackson into sole possession of 24th place on the career RBI list with 1,703. His 168 RBI against the Rays are the most by any Tampa Bay opponent.
Red Sox: IF-OF Brock Holt, out since May 19 with a mild concussion, hopes to rejoin the team this weekend. ... RHP Brandon Workman, who missed all of 2015 after having Tommy John surgery, threw at Tropicana Field on Monday and expects to begin a rehab assignment soon.
Rays: OF-DH Corey Dickerson said swelling and soreness in his left thumb has subsided enough to take batting practice in an indoor cage. ... RF Steven Souza Jr. (strained left hip) started on-field batting practice. ... OF Brandon Guyer (strained left hamstring) is on a rehab assignment with Class A Charlotte.
Tampa Bay president of baseball operations Matt Silverman said before the game that the entire organization -- from coaches and players to the front office -- shares responsibility for rough stretch that dropped the Rays a season-low 12 games under .500. "We all take great pride in the winning product we've been able to put on the field, and we haven't seen that to date," Silverman said. "We're all looking in the mirror trying to figure out what we can do to improve this, to right the ship, and all ideas are on the table."
Red Sox: RHP Rick Porcello (8-2, 3.93 ERA) seeks his ninth victory of the season. In addition to being tied for seventh in the AL in victories, he hasn't allowed more than two walks in any of his past 19 starts, the longest such stretch for a Red Sox pitcher since Curt Schilling did it over 33 starts from Sept. 20, 2005 to Sept. 20, 2006.
Rays: RHP Chris Archer (4-10, 4.70) has gone from an All-Star a year ago to leading the majors in losses. He's 1-7 with a 5.67 ERA in 12 career starts against Boston, his most losses against any opponent.