ST. PETERSBURG, Fla. - A night after combining for seven home runs and 14 runs, the Tampa Bay Rays and Boston Red Sox waged a scoreless battle of attrition Sunday afternoon at Tropicana Field.

It took 13 innings and 33 combined strikeouts by the two pitching staffs, 19 by the Rays, but the bats finally woke up as Red Sox left fielder Rusney Castillo delivered a bases-loaded single to score the game's only runs in a 2-0 Boston victory.

Neither team's offense was able to reward outstanding starting pitching performances from Tampa Bay's Drew Smyly and Boston's Rich Hill, but the Red Sox got to a pair of Rays relievers for four straight hits in the game-winning rally in the 13th inning.

Second baseman Dustin Pedroia started the outburst with a one-out single off losing pitcher Enny Romero, who was chased after giving up two more singles by shortstop Xander Bogaerts and first baseman Travis Shaw to load the bases.

Facing new pitcher Andrew Bellatti, the Rays seventh pitcher, Castillo ripped an offering to left to score Pedroia and Bogaerts.

"I just took the same approach I would in any other at bat," said Castillo, who was 3-for-5. "It was nice to score in that inning. I just kind of stayed disciplined and waited for a good pitch to hit and luckily I got one."

Heath Hembree (1-0) got the victory with one inning of relief, and Robbie Ross Jr. picked up his second save.

Boston center fielder Mookie Betts singled to extend his hitting streak to 18 games, longest active streak in the majors, and went 3-for-6.

Otherwise, Smyly and Hill had many in the 15,402 wondering where both team's offenses had gone after Saturday's fireworks.

Hill was starting his first game since 2009, and after his sterling performance he certainly won't have to wait as long for his next one. He pitched seven innings, allowed one debatable hit and struck out 10. He only allowed one leadoff batter to reach base, and retired the last eight he faced.

"Great outing," said Red Sox interim manager Torey Lovullo. "Gives up the base hit - which was questionable itself - and gives us seven solid innings. The first time he's started a major league game (in 6 years) and it's just a great story. All the hard work that he put in behind the scenes to get back here has paid off. Fastball command, secondary stuff was there, anytime he needed a big pitch he seemed to make it."

Hill confused the Rays with his offspeed stuff, particularly a slow wide-bending curveball, right from the start. He sandwiched a pair of pop outs to the catcher around a strikeout for a 1-2-3 first inning, setting the tone.

"I was able to keep the ball down and command my breaking ball the way that I wanted to and that enhanced the fastball," said Hill. "You get a lot more swings and misses with the fastball from the good command with the curveball. They both go hand in hand."

Hill nearly left the game after seven with a no-hitter. In the third inning, Rays catcher J.P Arencibia hit a playable grounder to short and the backhand side of Bogaerts, who couldn't come up with it. It was ruled a single, the only hit that Hill allowed.

Tampa Bay didn't get a runner to third base all game and every starter except center fielder Kevin Kiermaier struck out at least once.

"I think he has extra life to the fastball, not necessary locating that well, but got enough kind of sneak attack fastballs, because everybody was factoring the big breaking ball that we were not able to adjust to," Rays manager Kevin Cash said.

After Hill departed, six Boston relievers combined to allow just two hits in the final six innings and help hand Tampa Bay its 11th straight extra-inning loss, dropping them to 69-73.

Smyly matched Hill scoreless frame for scoreless frame. He pitched six innings, allowed just four hits - two were bloopers and one never left the infield - and tied a career-high with 11 strikeouts. He was lifted after throwing 97 pitches, 60 for strikes.

"I was able to get strike on and strike two early, for the most part, and then when I needed to bury a curveball, I buried a curveball or a fastball up in the zone," Smyly said.

In seven innings, the Rays bullpen gave up 10 hits and flirted with trouble before the Red Sox broke through.

NOTES: A day after hitting two home runs to reach 500 for his career, DH David Oritz got the day off Sunday. Ortiz is now just one of four players, and first non-New York Yankee, with at least 500 homers and three World Series championships. The others are Babe Ruth, Mickey Mantle and Reggie Jackson. ... Sunday's scoreless start was the 28th by the Rays, tops in the major leagues. ... It was the third time this season that both starting pitchers in a Rays game recorded 10 strikeouts. Prior to this season, that had only happened three times in the Rays club history. ... Since May 31, Red Sox SS Xander Bogaerts leads all major leaguers with a .345 batting average. ... The last left-handed pitcher to go at least six years between starts before Hill was Australian Brad Thomas, who started a game in 2001 for Minnesota and didn't start his next one until 2010 for Detroit.