Matsuzaka (7-5) gave up two runs in six innings, and that was too many against the stingy Diamondbacks staff.
"I don't know if that was his best game, but I had to throw my best game, or at least match zeros with him," said Johnson (4-2), who won his fourth straight decision.
"It was good to get this one," Quentin said. "No one wants to get swept at home."
Boston's first regular-season visit to the desert attracted three big, boisterous crowds. Sunday's crowd of 46,622 was split between members of Red Sox Nation and home fans decked out in the Diamondbacks' new "Sedona Red."
Asked about the ongoing chants of "Let's go Red Sox," Johnson grinned and said, "That wasn't Sedona Red up there? I thought it was Sedona Red."
The Red Sox are used to playing in front of big crowds. But they unraveled in the eighth, when the Diamondbacks scored three runs to blow the game open.
"I just threw it away," said Timlin, who made his first appearance after more than month on the disabled list with right shoulder tendinitis. "Bad error. There's really no excuse."
Chris Young added an RBI single to make it 5-1.
Boston manager Terry Francona stacked his lineup with seven righties and two switch-hitters. But it didn't matter against the 43-year-old Johnson.
"I don't think you're going to see a lot of guys saying, 'Randy Johnson pitching, he's getting older, let's run down to the ballpark, let's jump in the batter's box,"' Francona said. "He's got good stuff, had it for a long time."
Johnson gave up four hits, walked three and struck out nine, throwing a season-high 113 pitches.
"We were prepared to take him out after 100, 102 (pitches), but he felt good and went back out there," manager Bob Melvin said. "R.J. gave us a little bit more than we actually needed today."
"I've pitched against the Red Sox enough that I know they're pretty explosive," said Johnson, who improved to 16-7 lifetime against Boston. "But I had a game plan, stuck to it and made my pitches when I had to."
Johnson fell behind 1-0 on Mike Lowell's RBI double in the fourth. Down 1-2 in the count, Lowell fouled off three pitches before driving a 3-2 delivery down the left field line, easily scoring Manny Ramirez from first.
Matsuzaka (7-5) walked two leadoff hitters, and both scored.
"That seems like the usual pattern for me," Matsuzaka said through a translator.
Matsuzaka allowed two runs on four hits in six innings, walking four and striking out nine.
"Our team lost, but overall I feel like I'm improving," said Matsuzaka, who lost his third straight decision. "The quality of my pitches is getting better."
- Matsuzaka struck out twice in his first major league plate appearances. "I asked him if he wanted to hit cleanup," Boston manager Terry Francona said. "He said, 'Randy Johnson, no, no.' This might not be a true test." Red Sox fans gave Matsuzaka a standing ovation when he fouled off a pitch before striking out in the fourth.
- Arizona 1B Conor Jackson was charged with an error when umpires ruled that he obstructed Coco Crisp during a first-inning rundown. Crisp had been picked off first by Johnson.