The D-backs seemed to have a good approach against Boston starter Clay Buchholz early on, as they made the right-hander work hard for his outs.
"We put a lot of pressure on him from the first inning on," Arizona manager A.J. Hinch said.
An RBI single by Adam LaRoche in the first inning gave the D-backs a 1-0 lead.
Unfortunately for the D-backs, the Red Sox had little trouble getting to right-hander Ian Kennedy.
"Early on, I felt like he was pressing and trying to be too perfect and too fine with his pitches, and he fell behind a ton of hitters early," Hinch said.
One of those hitters was David Ortiz, who jumped on a 2-0 fastball in the bottom of the first and deposited it over the Red Sox's bullpen in right-center to give Boston a 2-0 lead.
Adding to Kennedy's frustration was the fact that Dustin Pedroia reached in front of Ortiz when Kennedy hit him with a two-strike pitch.
"Early in the game, I threw a fastball just to get the ball in play, and he squared it up," Kennedy said of the Ortiz homer. "I got too much plate. Those don't really bother me; it's the ones where they get consecutive hits in a row."
That would come in the third, when the Red Sox combined four hits with a walk to score three times and take a 5-1 lead.
"I think they have a tough lineup," Hinch said of the Red Sox. "They grind you and make you earn every strike. Very rarely do they have early outs."
The D-backs pulled to within 5-3 in the fourth, when Justin Upton drove home a pair with a double off the Green Monster in left.
After that, though, the D-backs could muster little in the way of offense. They had just two more hits the rest of the way, and four Boston relievers combined to throw 3 1/3 scoreless innings to close things out.
Both of Arizona's hits came in the sixth, when with two outs, Tony Abreu singled and Rusty Ryal doubled. Hideki Okajima, though, fanned Kelly Johnson to end the inning.
"Really, after the fourth, we didn't do much after that," Hinch said. "[Buchholz] settled in and made pitches. He lasted long enough to hand the game to the bullpen, and they completely shut us down. We had the one opportunity against Okajima in the sixth, and then that was about it. They did a nice job of adjusting as the game went along and shut us down."
Kennedy (3-4) has been one of the team's better pitchers all year, but he wound up allowing six runs on nine hits over six innings.
"Rarely do you consider a six-run outing a good start, but I felt like he managed himself pretty well on a night that wasn't perfect for him," Hinch said.
That was of little consolation to Kennedy.
"I was just not getting ahead of guys," he said. "It's tough against a lineup like this. You can't do that. I feel terrible, because my job is to keep us in the game, and I didn't do that."