Millwood held Boston scoreless for seven innings, Kinsler hit a three-run homer and the Rangers ended an eight-game losing streak in Fenway Park with a 5-1 victory over the Red Sox on Friday night.
"It's a different year," Kinsler said. "It's just another win. We're just trying to keep winning."
The AL West-leading Rangers have been in sole possession of first place for the past 31 days, their most since 1999.
"Well it's nice to get a win, yes it is," Rangers manager Ron Washington said. "We certainly weren't thinking about what happened last year. We're just out there trying to win a ballgame."
The Rangers, who dropped two of three games against the Yankees this week, lost all seven in Fenway last year and went 1-9 overall.
"I thought tonight was a big game for us," Millwood said. "To be able to go out and pitch well gives us a big boost. I've always liked pitching here. I know they're not cheering for me, but there's always a lot of energy in this ballpark."
The loss snapped Boston's four-game winning streak and dropped its home mark to 17-7, second in the majors behind the Los Angeles Dodgers.
The Red Sox stranded 13 runners, nine on second or third.
Millwood (5-4), winless in four of his last five starts, shut out the Red Sox until David Ortiz's RBI single in the eighth. Eddie Guardado relieved and retired the next three hitters easily with two runners on before Darren O'Day got the final three outs despite walking a pair.
Millwood gave up an unearned run, seven hits, struck out five and walked four. He escaped a pair of second-and-third, two-out jams in the first six innings as the Rangers built a 5-0 lead.
"He threw the ball good and made pitches when he had to," Boston catcher Jason Varitek said.
Texas had a four-run fifth. Elvis Andrus had a two-out RBI single just under the glove of shortstop Julio Lugo in the hole after Marlon Byrd and Chris Davis singled. Kinsler then turned on Penny's inside fastball and lined it into the second row of the Monster seats for his 15th homer, making it 4-0.
The Rangers chased starter Brad Penny (5-2) with a run in the sixth. Davis had a two-out RBI double after Byrd's single slipped under Lugo's glove on a ball up the middle.
Penny held the Rangers to a bad-hop infield single until the four-run fourth.
"His first four innings were as good as we've seen," Boston manager Terry Francona said. "He was throwing the ball really, really well. Then the next two I think he threw 50 pitches."
Penny allowed five runs, seven hits, walked two and struck out five in 5 2/3 innings. It was just the second time in his last seven starts he's given up more than three runs.
Boston, coming off its longest road trip of the season -- a 10-game stretch where it went 6-4 and swept AL Central-leading Detroit -- hardly threatened against Millwood in the first five innings. The Red Sox's best chance came in the third when Mike Lowell bounced out to end the third when Michael Young made a nice play to his right with runners on second and third.
Jacoby Ellsbury flied out with two runners on in the sixth.
Washington said he avoided going to closer Frank Francisco because "he said his shoulder was sore." ... Ortiz, mired in a season-long slump, will have his eyes check Monday. But Francona downplayed it before the game, saying the exam was routine. ... The Rangers were outscored 67-35 in their seven losses in Boston last year. ... Boston RHP John Smoltz, recovering from offseason shoulder surgery, will make his fourth rehab start on Saturday after his scheduled start with Triple-A Pawtucket was rained out. ... Red Sox 1B Kevin Youkilis was back in the lineup after leaving Thursday's win in Detroit early with tightness in his right calf.
New York Mets, Philadelphia Phillies minor leaguers protest low pay with wristbands
Minor league players in the New York Mets and Philadelphia Phillies farm systems are wearing wristbands Saturday to protest pay that they say is insufficient.
Semien's 40th homer lifts Blue Jays back into playoff spot
— Marcus Semien became the fifth second baseman to hit 40 home runs in a season, and the Toronto Blue Jays moved back into a playoff position by beating the Minnesota Twins 6-2 Saturday.
Marcus Semien crushes his 40th HR of the season
Marcus Semien goes deep for the 40th time this season to get the Blue Jays on the board.
Teoscar Hernandez busts a move in the dugout after three-run homer
Teoscar Hernandez shows off his dance moves after blasting a go-ahead three-run homer for the Blue Jays.
Josh Donaldson launches two-run dinger into the bleachers
Josh Donaldson gets the Twins on the board early with a two-run jack to right field.
New York Yankees left fielder Joey Gallo exits game with neck tightness
Yankees left fielder Joey Gallo left Saturday's game because of neck tightness. Manager Aaron Boone said he was unsure how Gallo's neck tightened up.