Jason Varitek drove in three runs and Manny Ramirez, David Ortiz and J.D. Drew all drove in two as the Sox matched their season high for runs, winnning their second straight and fourth in the past five after a five-game losing streak.
In the previous start, Shields threw 98 pitches in nine innings. On Saturday night, with a game-time temperature of 45 degrees chilling the air, it was 98 in 3 2/3 ineffective innings.
"Yeah, he just wasn't comfortable, he just didn't appear to be," said Tampa Bay manager Joe Maddon. "That would be the best word."
Dustin Pedroia and Ortiz both went 3-for-3 against Shields, who completed a sweep of the Red Sox last weekend.
Red Sox ace Josh Beckett, who lost to Shields last Sunday despite striking out 13, was anything but overpowering early in the rematch, but settled down and wound up going eight innings to raise his record to 3-2. He did surrender a pair of homers, but allowed just one run on two hits over his last 4 2/3 innings, and got a huge lift from his defense, notably Ramirez, who threw Carlos Pena out at the plate to complete a double play and end the fourth inning.
"They picked me up today," Beckett said. "Offensively, obviously with the number of runs and hits that we had but there were four great plays out in the outfield and Mike [Lowell's] play, [Kevin Youkilis] down the line, flipping me the ball, those are big things."
It was the first win by a Red Sox starter other than Clay Buchholz since April 20.
Ramirez's throw -- his second assist of the season -- cut off a run that would have made it 5-4.
"I think he has the uncanny ability to be unbelievable accurate," Francona said. "He has the ability to sometimes not move his feet, not that he didn't there, but look left, throw right and the ball ends up right where it's supposed to. I've always thought he could do that since I've been here and I didn't see him before.
"It's a pretty good play at an important juncture of the game."
From there, the Sox took off.
"Tonight's game ends up being 12-4, but in the fourth inning we're up 5-3 and they have the bases loaded," said Francona. "We get a lineout, then we get [another] lineout [after a walk], Manny throws a guy out at the plate and then we score two, and the game changed drastically. Sometimes you catch a break and then you take advantage of the breaks."
The first four Red Sox hitters collected hits against Shields (3-2) as Ortiz drove in a run with a double and Ramirez followed with a two-run single, ending an 11-game RBI-less streak, his longest in a Red Sox uniform.
Gabe Gross got two of the runs back with a two-run homer off Beckett in the top of the second, but the Sox scored single runs in the second and third and, after Tampa Bay scored in the fourth, Boston tallied twice in the bottom of the inning and then added two more in the sixth and three in the eighth.
After batting .153 and scoring four runs in their previous five games, the Red Sox have 19 runs and 28 hits in the last two games. They had four extra-base hits during the five-game hitting drought, but have 11 in the last two games -- stroking six doubles Saturday night as they opened a two-game lead in the AL East.