Red Sox starter Eduardo Rodriguez, who allowed two runs over six innings, was appreciative for the early run support.
"It changes for everybody [that pitches]," Rodriguez said. "He goes up there and hits the homer, you feel a little bit better every time. When somebody does that, it's 1-0 already, and you try to keep the [opponent] at zero."
Betts has six home runs this season, four of which came during this series.
Betts' performance has been part of a power surge for the Red Sox to open their three-city, nine-game road trip. His leadoff homer was Boston's 10th home run of the series, then Andrew Benintendi went deep later in the game for No. 11.
"It was a 2-0 slider, he stays on it, and it's 1-0 us," manager Alex Cora said of Betts' leadoff homer. "He's putting pressure on the opposition from pitch one. That's what we had in mind from the get-go, and he's executed."
Betts has reached base to begin eight of the 16 games he has started in the leadoff spot. He also has a hit in 13 of his last 15 games.
"I'm just trying to get on base, or do something to help score a run," Betts said. "That's why you're up there, to score runs, and I know that. I'm just trying to do something to impact the game, and a couple went over the wall."
Betts might make it sound simple, but his start to the season has made franchise history. His 22 runs scored moved him past Johnny Pesky (21 in 1950) and Ted Williams (21 in 1942) for the most by a Red Sox hitter through 18 games since at least 1908.
"Obviously, [the confidence] is really high in every game we play in," Betts said. "We feel like we have a chance to win. That's all you can really ask. The pitchers are doing great and giving us hitters the opportunities to help win games. We're having some timely hits, and we have to build on innings throughout the game, not just late. It seems like we can score at any given time."