None of the hits were home runs, but it didn't seem to matter as the Sox, who lead the Major Leagues in runs scored, got to Colorado starter Juan Nicasio early and often.
He was forced out of the game after just 2 1/3 innings as he gave up seven runs (six earned) and 12 hits.
"Outstanding performance," Red Sox manager John Farrell said. "Anytime you get 20 hits it's a very good night, but I think early on we found some holes with some base hits that weren't squared up and then combined it with some balls that were squared up."
Six Red Sox reached based at least three times Tuesday, their most in a nine-inning game since Sept. 19, 2011.
One of the six was the newly minted everyday third baseman Jose Iglesias, who knocked three hits in five at bats and scored two runs. Just hours earlier, the Red Sox made the decision to send Will Middlebrooks down to Triple-A Pawtucket, giving Iglesias the chance to start on a daily basis for the first time in his Major League career.
"It's good to have the opportunity to play every single day," said Iglesias, who is now batting .434 on the year. "It kind of surprised me, you know? I never think of playing third in my life and now you get a chance to play here."
Iglesias was part of a Red Sox attack that scored and had at least three hits in each of the first four innings. They were not retired in order until the sixth.
Dustin Pedroia went 3-for-5 with four RBIs and also converted a pair of impressive defensive plays, adding on to what is already an impressive Gold Glove resume this season.
Two other Red Sox -- Jacoby Ellsbury and Daniel Nava -- had three-hit nights and every batter in Boston's starting lineup had at least one.
All of it was in support of Red Sox starter Ryan Dempster, who went for his sixth quality start in a row and pitched six innings of two-run baseball.
He surrendered a towering home run to Wilin Rosario in the second that flew well over the Green Monster, but, as has been customary with Dempster this season, it was only a solo shot. Of the 17 long balls Dempster has given up this season, 15 have come with no one on base.
"I've always said solo home runs don't beat you," Dempster said. "I wish there haven't been that many I've given up, but you know especially in a situation like tonight where we're putting up runs, I'm trying to attack the strike zone and if somebody hits one out they hit one out."
The effort earned him his fifth win of the season and lowered his ERA to 4.15.
The Red Sox wasted no time getting started offensively. Pedroia singled in Ellsbury, who led off with a double, in the first. Back-to-back walks to David Ortiz and Mike Napoli loaded the bases and a flare off the bat of Nava scored another run.
Nicasio retired the first two batters in the second, but then gave up five straight hits, including three consecutive doubles from Shane Victorino, Pedroia and Ortiz, as the Sox added three more runs to their lead in the second.
"Yeah it just looked like he struggled to find a rhythm tonight," Colorado manager Walt Weiss said of Nicasio. "He was in bad counts and it's a tough club to be in bad counts with. If you're going to get a fastball in fastball counts, these guys aren't going to miss it."
Stephen Drew appeared to hit a home run in the sixth. The ball hit the top of the wall just to the right of the Green Monster before coming back into play, but after a lengthy review process, it was ruled a triple.
On a different night, the sequence might have been more controversial, but on the very next at-bat, Iglesias doubled him in. It was that kind of night for the Red Sox.
Colorado added two unearned runs in the seventh off Alex Wilson. In the inning, Victorino collided with the right-field wall and dropped a fly ball hit by Jonathan Herrera.
Charged with an error, Victorino momentarily stayed on the ground after the play as Nolan Arenado scampered home. Victorino, who left Sunday's game against Detroit with back tightness, was examined by a trainer, but remained in the game.
"Well, another wall another day," Farrell said. "He hit a bolt that holds up one of those signs and it's not that he suffered a gash but it hit him in a tough spot right above the ear. Kind of lost his footing going after the ball and like I said it seems like he's finding a wall on a daily basis."
Michael Periatt is an associate reporter for MLB.com.