The Rockies also will be trying to avoid their first four-game losing streak since enduring an eight-game skid, June 22-29.
Against these Red Sox, it's proving to be a daunting challenge.
"They're clicking on all cylinders right now, like we were the last two [playoff] series," Rockies third baseman Garrett Atkins said. "They're pitching well, they're getting hits when they need to and they're playing good baseball.
"We have to try to match them. Tonight, we took a step in that direction."
The destination, however, is a long way off. The Rockies matched the 1976 Reds as the only clubs to win their first seven playoff games, although that seems long ago. The Rockies hope their revival starts Sunday night with right-hander Aaron Cook, who started on Opening Day but has been out since Aug. 10 with a strained left oblique.
"OK, so we're in groundbreaking territory," Rockies manager Clint Hurdle said. "I mean, we've got to go out and win Game 4."
The Rockies scored all their runs in the sixth and seventh. Holliday's homer off Hideki Okajima in the seventh brought the Rockies to a 6-5 deficit, before the Sox added three runs off Brian Fuentes in the eighth and one off LaTroy Hawkins in the ninth.
Still, it's an improvement for a club that scored just one run in each of the first two Series games. The Rockies struck out seven times to bring their three-game total to 29, but they had a healthy 11 hits.
"We've got to build on something," first baseman Todd Helton said. "They've got their foot on our necks right now and they're going to grind it in there a little bit. So we've got to stop the bleeding right now."
After falling behind 6-0, all the runs scoring against Rockies starter Josh Fogg in the third, the Rockies' offense finally produced.
At the start of the sixth, Helton and Atkins drew walks from winning pitcher Daisuke Matsuzaka, who held the Rockies to three hits in 5 1/3 innings and drove in two runs with a single -- his first Major League hit.
Brad Hawpe and Yorvit Torrealba added singles off Javier Lopez to get the Rockies on the scoreboard, but then the scoring chances faded away despite two hard-hit balls. Ryan Spilborghs flied to deep center -- it looked like it would travel farther, but died at the wall. Sox shortstop Julio Lugo then robbed the Rockies by leaping to grab Jeff Baker's screaming line drive to end the inning.
"It's a game-changing play -- two outs, we're probably going to send that guy from first and it's probably going to go into the gap," Baker said. "It's a two-run swing right there."
Kazuo Matsui, who had three hits while replacing Willy Taveras in the leadoff position in Hurdle's revamped lineup, and Troy Tulowitzki singled off Javier Lopez to set up Holliday's fifth homer of the postseason, to dead-center off Okajima.
Holliday also came up with two on and two out in the eighth, and launched one to deep left against closer Jonathan Papelbon that caused halted breaths but was merely the final out of the inning.
"We just got some confidence," Holliday said. "Now we've got to come back tomorrow and try to score some runs."
"There comes a point in time when you've got to find ways to score runs, you've got to find ways to get outs and you've got to find ways to make pitches. They've been able to do that a little more consistently than we have."
-- Rockies manager Clint Hurdle
Close calls didn't help the Rockies, either. In addition to the Baker liner and the fly balls by Spilborghs and Holliday, they lost two runs in the eighth when Hawpe slid near the foul line but Jacoby Ellsbury's blooper ticked off his glove for a two-run double. It was one of Ellsbury's four hits from the leadoff position, and No. 2 hitter and fellow rookie Dustin Pedroia added three hits.
The Rockies hadn't hit much all postseason, so until meeting the Sox in the Series, their pitching carried them.
But on Saturday, Fogg lasted just 2 2/3 innings. No starter has made it as far as five innings thus far. Jeff Francis gave up six runs in four innings in the 13-1 loss in Game 1. Ubaldo Jimenez gave up just two runs but walked five and lasted just 4 2/3 innings of the 2-1 loss in the next game.
"I gave up six runs in two-third innings -- that's a poor performance," Fogg said. "That's the key to baseball: getting good starting pitching. Obviously, they've done it and we haven't."
Matsuzaka's two-run single, which made it 5-0, is an example of how poorly things have gone for the Rockies.
It left Matsuzaka with double the postseason RBI total of Atkins, who had 111 during the regular season; even with Helton, who had 91; and temporarily tied with Hawpe, who drove in 116 during the regular season. Hawpe's RBI in the sixth brought his postseason total to three.
"There comes a point in time when you've got to find ways to score runs, you've got to find ways to get outs and you've got to find ways to make pitches," Hurdle said. "They've been able to do that a little more consistently than we have."