Hunter allowed one run and four hits over six innings to beat All-Star Josh Beckett, who still threw his third complete game in six starts, in the Rangers' 4-2 victory.
"He kept his composure," Rangers second baseman Ian Kinsler said of Hunter. "He's matured so much since last year."
Boston has its first four-game losing streak since last July, scoring only eight runs in the stretch. The New York Yankees beat Baltimore 6-4 on Tuesday night to break the tie atop the AL East, where the Red Sox had been since June 9.
"We've hit our worst spot of the year as a team swinging the bats," Red Sox captain Jason Varitek said. "We've all been here before. We're one or two hits away from getting it back together."
Boston, which lost two of three at Toronto over the weekend, has lost consecutive series after winning five in a row before the All-Star break.
Hunter (2-1), a 23-year-old right-hander drafted only two summers ago, gave up nine runs in 1 2/3 innings at Fenway Park last August in one of his three starts last season.
"I did not throw well when I pitched against them last year. I threw pretty well tonight, I was able to throw four pitches for strikes," Hunter said. "Last year, I had a pitch-and-a-half. I wouldn't consider the fastball a pitch, it was always up in the zone."
The Red Sox weren't able to tee off this time against Hunter, who threw a lot of changeups.
"They hit a lot of weak pop flies," he said.
Boston's only run against Hunter came in the sixth when Dustin Pedroia had a two-out single and Kevin Youkilis followed with a double into the right-center gap. David Ortiz, who had been thrown out in the second trying to extend a leadoff single, then hit an infield popup on Hunter's last pitch.
"He had given us what we needed," manager Ron Washington said.
Hank Blalock put Texas ahead to stay with a two-run single in the first, though the Texas-born Beckett (11-4) retired 13 batters in a row after that until Michael Young's one-out single in the sixth.
"I didn't make very good pitches. This one falls on me. I think the right person got the loss," Beckett said. "The game was lost in the first inning. Two-out runs are demoralizing to everybody, especially to a pitcher. ... It's unacceptable."
Kinsler had a leadoff double and Jones a two-out walk in the first before both advanced on a double steal. Blalock then pulled a liner through the right side of the infield.
Beckett struck out seven and gave up seven hits in his first start since July 12. He threw a three-hit shutout at Kansas City before the All-Star Game, where he didn't pitch.
The right-hander was 4-0 with a 1.63 ERA his previous five starts, including another shutout. He had been 6-0 in games following Boston losses.
C.J. Wilson worked the ninth for his ninth save in 11 chances, despite giving up an RBI single to Mike Lowell. Wilson has saved both games since closer Frank Francisco was put on the disabled list for the third time this season -- this time with a case of pneumonia.
Rangers relievers have allowed one run in 14 innings in a three-game winning streak that has followed a four-game slide.
- Kinsler caught two inning-ending popups in foul territory. He reached into the stands to end the fourth to catch Jason Bay's popup when the bottom half of his body crashed into the 3 1/2-foot high brick facade.
- Boston is 8-15 vs. the AL West.
- Rangers All-Star OF Nelson Cruz, out of the starting lineup for the third consecutive game with a fractured right ring finger, took some swings before the game and could be back in the lineup Wednesday.
- Texas LHP Matt Harrison, out since May 26 because of left shoulder inflammation, will make a rehab start Wednesday for Double-A Frisco.