Lester (13-7) stayed ahead of a potent lineup throughout, mixing four pitches to scatter five hits while striking out five and walking none. The All-Star left-hander threw 109 pitches while experiencing nausea due to the heat.
"We needed him to go out there and pitch exactly like he did," Boston manager Terry Francona said. "I think the heat got to him a little bit. He was queasy and a little sick to his stomach. ... I don't think he felt good all night, but he said something about it in the sixth."
The Red Sox hoped for a lengthy outing from Lester because top relievers Jonathan Papelbon and Daniel Bard were unavailable after pitching in the previous two games.
Lester was up to the task, and he even wanted to take a shot at his third complete game of the season before he was overruled by his manager.
"I try to finish the game every time I pitch," Lester said. "Obviously I know what the situation is and it would be nice to go deep in the game, but you're not out there trying to press and say, 'I got to do this.' I was just trying to take it one pitch and one inning at a time and I was able to do that tonight and give the bullpen a little break."
Boston has scored only eight runs during Lester's last six starts. This time, he didn't need much support.
"We needed this game. ... and the next game. We need every game the rest of the year," Boston's Bill Hall said.
Josh Hamilton homered with one out in the ninth off Red Sox reliever Scott Atchison. Hamilton went 2 for 4, raising his major league-high average to .364.
Rookie Felix Doubront got the final two outs for his first career save.
Colby Lewis (9-9) struck out nine and walked two while allowing one run and six hits over 6 2-3 innings. He lost his fourth consecutive decision.
Like Lester, run support has been a recent issue for Lewis, who's lost his last four starts. Texas has scored seven runs in his last five starts.
"You've got to roll with the punches," Lewis said. "If I go out there and give a quality start and keep my team there, we're one swing away from getting a win."
Boston ended a two-game skid a day after Texas' 10-9 victory in 11 innings in which the Rangers rallied from a season-high six-run deficit.
In the Red Sox fifth, Ryan Kalish had a leadoff single, went to second on a passed ball by Taylor Teagarden, advanced to third on Marco Scutaro's infield single and scored on J.D. Drew's bloop single for a 1-0 lead.
Texas had a chance to draw even in the seventh when Nelson Cruz tripled with one out. But Lester retired David Murphy and Jorge Cantu on groundouts.
Cruz slowed while running to third, and was lifted from the game at the end of the inning with tightness in his left hamstring.
Cruz will be evaluated on Sunday. He's already already made two trips to the disabled list this season with strains of both hamstrings.
Hall's RBI single in the ninth off Darren O'Day stretched Boston's advantage to 2-0. That stopped O'Day's club-record scoreless streak of 29 games, a span of 26 1-3 innings.
Boston made it 3-0 on Scutaro's sacrifice fly, with Scutaro safe at first when Texas center fielder Julio Borbon dropped the ball.
The Red Sox were without center fielder Jacoby Ellsbury, who went on the 15-day disabled list for the third time this season with more bruising of his left ribcage.
Ellsbury underwent an MRI exam and CT scan in Boston on Saturday, with the diagnosis that he reinjured his ribs in a collision at first base in the first inning on Friday night.
NOTES: The teams wrap up the three-game set Sunday, which is projected as one of the hottest days of a scorching North Texas summer with a predicted high temperature of 105. ... Rangers CEO Chuck Greenberg and team president Nolan Ryan participated in the ceremonial first pitch in recognition of major league approval of the new ownership group on Thursday. Greenberg did the pitching and Ryan, the Hall of Fame RHP, was the catcher. Ryan made a short-hop scoop of Greenberg's low pitch. ... Texas C Matt Treanor will begin a rehab assignment with Triple-A Oklahoma City on Monday. ... The Rangers placed 2B Cristian Guzman on the 15-day DL with a strained right quadriceps and recalled RHP Pedro Strop from Triple-A Oklahoma City. ... Red Sox 2B Dustin Pedroia went 1 for 3 on Saturday night in a rehab assignment as Triple-A Pawtucket beat Buffalo, 6-4. Pedroia is on schedule to be activated from the 15-day DL next week in his comeback from a broken bone in his left foot. ... Boston C Victor Martinez went 0 for 4 to snap an 11-game hitting streak.