Three of the shutouts have come since July 8. This is unfamiliar territory for a team that went scoreless six times in all of 2016, and is usually known for its offense.
The good news for the Red Sox is that they are still in first place in the American League East, with a two-game lead over the Yankees.
But the bats will need to start functioning more consistently if that lead is going to hold, or be extended.
"Just the inability to string base hits together," said Red Sox manager John Farrell. "We do it on the first game of this road trip and that's the type of offense we're capable of, but to sustain it, that's where it's been a little hit and miss. We're not built around the home run. We recognize that. We know there's got to be quality at-bats up and down the lineup and that has shown itself to be the case in some innings, but others it's not."
While homers are on an uptick around the Majors, it hasn't spread to the Red Sox, who are last in the American League with 99.
When the Red Sox do hit at least one homer in a game, they are 38-23. When they don't, they are 17-23.
Top prospect Rafael Devers, who will make his Major League debut for the Red Sox on Tuesday, has 20 homers in the Minors this season. Perhaps he can help.
Mookie Betts (17) and Hanley Ramirez (16) are Boston's only players with more than 15 homers this season.
But it's unfair to expect Devers can turn the lineup around by himself.
"It falls on everybody," said Dustin Pedroia. "It's a team. We win as a team, we lose as a team. It's 25 guys. It doesn't fall on me or Hanley or anybody like that. It's everybody. We do it together."
For the first time since May 18-20, the Red Sox have lost three in a row. They've scored a total of five runs in the three losses. Since the All-Star break, Boston has scored 39 runs over 12 games, scoring three runs or less in seven of those contests.
"You can catch a cold streak but you can catch a hot streak just as fast," said Pedroia. "You've got to stay positive, keep working and just find a way."
From Betts to Andrew Benintendi to Pedroia to Ramirez to Jackie Bradley Jr. to Xander Bogaerts, the Red Sox have a collection of accomplished hitters. But to this point, the unit hasn't added up to enough firepower.
The Red Sox are sixth in the AL in runs scored, but 14th in slugging percentage.
"Our offense is built as it is and we can't come out of that approach," said Farrell. "I don't see guys looking to try to leave the ballpark with big swings. It's a matter of staying in the middle of the field and putting quality at-bats together. We're a team that's got to be built with consecutive base hits and right now that's been hit and miss."