Trevor Story, right, is congratulated by Christian Arroyo after hitting a solo home run in the fourth inning of Boston’s 4-0 win over the Tampa Bay Rays on Monday at Fenway Park. Mary Schwalm/Associated Press

BOSTON — Trevor Story hit a solo homer, Kutter Crawford pitched 5 1/3 innings of two-hit relief and the Boston Red Sox won their eighth straight Fourth of July game, beating the Tampa Bay Rays 4-0 on Monday.

Franchy Cordero added an RBI single for the Red Sox, who won their second straight game and improved to just 9-16 against AL East rivals.

“Kutter gave us a lot, helped us out a lot in the pen there,” Story said. “He looked great.”

With a handful of its players wearing long sleeves with stars and stripes on a warm, sunny day, Boston matched its franchise record for consecutive July 4 wins, accomplished from 1901-04 and 1936-39, when teams played doubleheaders.

Tampa Bay had its three-game winning streak halted and lost a road series opener for the eighth straight time. The Rays had just two hits, both singles.

“Kutter Crawford, we’ve seen him twice now and he’s pitched really well against us,” Rays Manager Kevin Cash said. “Big fastball, threw the breaking ball and had the cutter as well. We just couldn’t get anything going. Just never felt like we had a rhythm at the plate at all.”

Story put the Red Sox ahead in the fourth, driving a changeup from Josh Fleming (2-4) into the back of Boston’s bullpen for his 13th homer.

Boston went with a bullpen game because scheduled starter Michael Wacha was scratched Sunday with what Manager Alex Cora called a dead arm. The Red Sox started Austin Davis for two hitless innings before using two more relievers.

Crawford (2-2) struck out eight and walked one and John Schreiber got five outs for his third save.

“I had pretty good command of all five of my pitches,” Crawford said. “I was just going right at guys. When I fell behind on the count, I got right back into it with the cutter or curveball. … The last couple of outings I figured something out that’s helped me mechanically.”

The Red Sox added a run in the fifth when Christian Arroyo doubled leading off, advanced on a groundout and scored when Rafael Devers was credited with an infield hit after second baseman Isaac Paredes bobbled his grounder trying to make a backhand pickup. Fleming booted a comebacker with the bases loaded for a run before Cordero’s single.

Fleming gave up four runs in five innings of relief.

TOUGH STRETCH

Boston opened a stretch of 27 games against teams with winning records.

“Just as important as the first 70 or whatever we played,” Cora said. “With our ups and downs and, obviously how we struggled early in the season, if you look at the standings, we are where we’re at.”

In addition to the Rays, Boston faces the Yankees, Houston, Milwaukee, Cleveland and Toronto during the run.

I’LL TAKE CARE OF IT

Tampa Bay’s Yandy Díaz got caught rounding first too wide on his bloop hit to right. Crawford, who came in to cover first, took the throw and sprinted after Díaz before making the tag himself.

“Yeah,” he said, breaking into a wide smile when asked if he was showing his 40-yard dash speed.

RAYS SHUFFLE ROSTER

In addition to Raley and Thompson returning, the Rays recalled LHP Josh Fleming from Triple-A Durham and returned RHP Phoenix Sanders and RHP Javy Guerra there. RHP Cristofer Ogando was optioned to Durham.

TRAINER’S ROOM

Rays: Reinstated LHP Brooks Raley and RHP Ryan Thompson from the restricted list.

Red Sox: LHP Chris Sale (out since spring training, stress fracture in his ribcage) is set to make a rehab start for Triple-A Worcester on Wednesday. “Feels good,” Cora said. “One, maybe two more down there.” … Cora also said Wacha would be checked out. “We don’t believe there’s something structural there, just kind of like a dead arm,” the manager said. … Nathan Eovaldi (injured list, back) and Garrett Whitlock (IL, hip) are both slated to throw off the mound Tuesday.