Bogaerts keyed a three-run rally by the Red Sox in that sixth, as they climbed out of a 2-0 deficit.
• Cast your Esurance All-Star ballot for Bogaerts and other #ASGWorthy players
"We had some key at-bats," said Red Sox manager John Farrell. "Bogey, an 11-pitch at-bat, finally gets the base hit. We would get down in the count, but we wouldn't give in, wouldn't give at-bats away. That's the characteristic that this group has really developed throughout the course of the year. We were able to extend some at-bats. We get a break with a hit by pitch. Just in that inning, like I said, we just didn't give in."
Bogaerts has the longest active streak in the Majors and second best this season after teammate Jackie Bradley Jr., who had a 29-game streak snapped on Thursday against the Rockies.
• Play Beat the Streak, win $5.6 million
Even after going 1-for-6 on Sunday, Bogaerts leads the American League with a .351 average.
Bogaerts has been a consistent force for the Red Sox the past two seasons.
"The one thing that's different is, because he's handled pitches away from him so well, there's been more pitches that he's seeing on the inside part of the plate, and he's pulled his hands in routinely with good, hard contact to the pull side," said Farrell. "We're seeing some of the power that everyone had alluded to, and that's by a natural progression that we felt would take place."
Ian Browne has covered the Red Sox for MLB.com since 2002. Follow him on Twitter @IanMBrowne and Facebook. This story was not subject to the approval of Major League Baseball or its clubs.