This marked just the second time in the last 12 games the Red Sox have been able to score more than four times.
"We kind of did spread it out," said Red Sox manager Terry Francona. "They get a couple, but we come right back, take some good swings. That was important."
So, too, was the pitching performance of Clay Buchholz. The righty worked seven strong innings, giving up five hits and a run while walking one and striking out seven. The first-time All-Star is 11-5 with a 2.71 ERA.
With the Yankees and Rays both securing wins before Boston even took the field, this was a win that Francona's team desperately needed, as the Sox stayed five games behind the Rays in the Wild Card standings and eight in back of the Yankees in the American League East.
"We need to win ballgames," said Red Sox right fielder J.D. "It doesn't matter who it's against."
Ortiz's second homer of the night -- a two-run missile to right-center in the eighth -- gave Boston's pitching staff at least some semblance of breathing room for the first time in a few days, and they needed it, as Hideki Matsui's two-run shot off Scott Atchison made it a one-run game in the eighth.
Drew gave the Red Sox another big hit in the ninth, a two-run double off the top of the wall in right.
"Just a fastball. He got 3-2 and I don't think he wanted to take a chance walking me and the pitch was a little bit up, and I got the barrel to it," said Drew. "I put a lot of topspin on it. A couple of more inches, we're all right, but that worked out pretty good."
On a night ace setup man Daniel Bard was unavailable, Jonathan Papelbon produced his first four-out save of the season.
"As much as we like Bard, our goal is not to have him leading the league in appearances and innings," Francona said. "Some nights, you've got to win without him. I'd rather it have been three [outs for Papelbon]. As soon as the tying run came to the plate, Pap knew he was in the game. Three is a lot better. That's a long inning in between, a lot of waiting, but sometimes you've got to do it."
Dan Haren, starting for the Angels just one day after being traded over from the D-backs, had to leave the game in the fifth inning when Kevin Youkilis stung a line drive off his right forearm. The righty was diagnosed with a contusion and will be reexamined on Tuesday.
Haren gave up seven hits and two runs over 4 2/3 innings, walking none and striking out eight.
"He was getting ahead of hitters," said Angels manager Mike Scioscia. "They came out and bunched some hits together, but he really minimized the damage early and then gave up a home run to Ortiz. But other than that he pitched terrific and it's unfortunate his outing was cut short."
It was the Angels who struck first, with Bobby Abreu rifling a solo shot to right with two outs in the bottom of the first.
But the Red Sox didn't take long to answer. Adrian Beltre led off the second with a triple to center that Torii Hunter nearly made a brilliant catch on. Victor Martinez, in his first at-bat back from the disabled list, ripped Haren's first pitch up the middle for an RBI single to tie the game. Jed Lowrie's double gave the Sox second and third with nobody out, but they couldn't push another run across.
Buchholz then got into a bases-loaded, nobody-out jam in the bottom of the second, but somehow escaped with no runs across.
"That doesn't happen all the time," said Buchholz. "The only guy that does that on a consistent basis is Daisuke [Matsuzaka]. It's unbelievable. Sometimes, you're sitting there and watching and he just finds a way to get out of it. That's why he's as good as he is. You're hoping to just minimize damage, maybe give up one or two runs and get out of it with nothing else happening. That was the [key] point of the game. We got into the dugout, scored a couple runs and the rest was history."
Ortiz gave the Sox their first lead in the top of the third, roping a solo homer to right, No. 20 on the season. It marked the ninth straight season Ortiz has belted 20 long balls, the last eight of them coming for Boston.
"We need him," Francona said. "He's a big bat for us. We need him. He hits right smack in the middle of the order. He's a big part of what we do. Tonight he was a real big part."