Ian Kinsler drilled his 15th home run of the season for the Rangers (32-22), who used a four-run fifth inning to back Millwood (5-4). The veteran righty, who improved to 4-1 lifetime in eight career starts at Fenway, has logged six or more innings in 11 of his 12 starts this season.
"I like this ballpark," Millwood said. "There's always a lot of energy here. Obviously they're not cheering for me, but when there's a lot of energy, I think I feed off of it. It just makes it a fun place to pitch."
Elvis Andrus ignited Texas' scoring barrage in the fifth, lining a 3-2 fastball from Boston starter Brad Penny (5-2) under the glove of a diving Julio Lugo to score Marlon Byrd. Two pitches later, Kinsler turned on a Penny offering and yanked it into the Monster Seats for a three-run homer.
"That home run was huge because it gave us some cushion," Texas manager Ron Washington said. "From there, we were able to make pitches and get out of the game."
Chris Davis extended the Rangers' lead in the following inning, unloading an RBI ground-rule double to right field for an insurance run that proved inconsequential.
The Red Sox (32-23) scratched a run across in the eighth against a tiring Millwood (117 pitches), as David Ortiz plated Jason Bay with an RBI single to right.
Eddie Guardado relieved Millwood and promptly extinguished a two-on, none-out jam in impressive fashion. The lefty retired Jason Varitek (strikeout), Jacoby Ellsbury (flyout) and Rocco Baldelli (groundout) in order to end the frame.
"If he gives up a couple runs there, all of a sudden it's a tight game again," Millwood said. "Eddie came in and shut them down. It was huge."
With two games remaining on their daunting six-game road trek through New York and Boston, the Rangers already consider themselves one of the best teams in baseball. Convincing the rest of the league of that fact has become their season-long mission.
"We feel like we're where we should be," Millwood said. "We have a good team, and we can play with anybody. The more we go out and play like we did tonight, the more people will realize it."