Dustin Pedroia ignited Boston's rally with a one-out single off Enny Romero. Xander Bogaerts followed with a single to center before Travis Shaw singled to right to chase Romero.
Andrew Bellatti took over and Castillo hit an 0-1 pitch to left field to drive home Pedroia and Bogaerts.
"Especially in a scoreless game, it was definitely a good feeling to get some runs on the board," said Castillo, who finished 3-for-5 with a double and a walk. "I just took the same approach as I would every other at-bat. It was nice to score in that inning. I stayed disciplined and looked for a good pitch to hit, and luckily I got one."
Left-handers Rich Hill and Drew Smyly seemed to be the mirror image of one another as they posted one zero after the next on the Tropicana Field scoreboard. Smyly did not allow the Red Sox to score in six innings, while Hill held the Rays to one hit -- an infield hit in the third by J.P. Arencibia -- en route to seven scoreless innings. Despite the fine outings, each came away with a no-decision.
"Commanded my breaking ball the way I wanted to, and that enhanced the fastball, so I got a lot of swings and misses with the fastball from the good command with the curveball," said Hill, who was making his first big league start since 2009. "The bullpen was immaculate and fielding was great, and Sandy [Leon] was great behind the dish. It was a good team win."
Each side used six additional pitchers to cover the remaining innings.
"Obviously, well-pitched game on both sides," Rays manager Kevin Cash said. "We came up on the short end of it there in the end, but our pitchers were outstanding."
MOMENTS THAT MATTERED Return to the Hill: The 35-year-old lefty, who was making his first Major League appearance of the season, was nothing short of spectacular, limiting the Rays to one hit over seven shutout innings with 10 strikeouts and a walk. Hill featured a four-seam fastball that sat consistently at 92 mph, along with a sweeping curve that he used to record seven of his 10 punchouts.
"Great outing. Just a great story," beamed Red Sox interim manager Torey Lovullo of Hill's performance. "He gives us seven solid innings. First time he's started a Major League game. … You can see that all the hard work that he put in -- everything that he did behind the scenes to get back here -- paid off. Fastball command, the secondary stuff was there, and any time he needed a big pitch, he seemed to make it." More >
Smyly ties career high: Scouts say hitters have a hard time picking up Smyly's pitches, and the left-hander affirmed that sentiment on Sunday when he struck out 11 in six innings. In the process, Smyly tied a career high for strikeouts in a game (he also struck out 11 against the Angels on July 25, 2014), and he reached double-digit strikeouts for the second time in three starts. More >
More Mookie magic: The Red Sox's center fielder ran his hitting streak to a Major League-leading 18 games with a third-inning single off Smyly. Mookie Betts, who went 3-for-6 on the day while collecting his 19th stolen base, is hitting .395 with seven doubles, a triple, four home runs and 13 RBIs during the stretch.
Strikeout city: Red Sox and Rays pitchers combined for 33 strikeouts on the afternoon, with Smyly and Hill accounting for a majority of the damage. The only starter for either club who didn't strike out at least once was Rays center fielder Kevin Kiermaier, who went 0-for-4 with a walk. Fittingly, the afternoon ended with Robbie Ross Jr. striking out Asdrubal Cabrera for the game's final out to earn his seventh save. The 19 strikeouts by Tampa Bay pitchers matched the club's all-time high at Tropicana Field.
QUOTABLE "Yeah, it's pretty brutal. It seems like almost every game is a save situation, which means we're in it. And then these extra-inning games, we just can't get the big hit. I mean, I don't know if the pitching is good or what, but it's tough when you lose by [one or two runs] so many times." -- Smyly, when asked about the Rays' 11-consecutive losses when they've gone to extra innings
SOUND SMART WITH YOUR FRIENDS For just the sixth time since 1914, both starters recorded at least 10 strikeouts and no runs. Rudy May of the Angels and Vida Blue of the A's were the last AL pitchers to turn the trick, which they did on July 9, 1971.
UNDER REVIEW The Rays challenged a call in the fifth inning after Richie Shaffer led off and appeared to get hit by a pitch on his left hand, but the call on the field was foul ball. After a review of 1 minute and 46 seconds, the call was overturned. Shaffer took his base and the Rays kept their challenge.
WHAT'S NEXT Red Sox: Lefty Eduardo Rodriguez (9-5, 4.05 ERA) will take the ball in Baltimore on Monday when the Red Sox open up a three-game series with the Orioles at 7:05 p.m. ET. The 22-year-old rookie, who is 0-1 with a 5.58 ERA in two starts vs. the O's this season, has notched a 3-0 record and 1.79 ERA in his last four trips to the hill.
Rays:Erasmo Ramirez (10-5, 3.96 ERA) will start as the Rays begin a three-game series against the Yankees. He has won both of his starts against the Yanks this season, yielding a combined four hits and one run over 11 innings.