MINNEAPOLIS -- Two weeks after a series against the Minnesota Twins sent them on a long slide, the Red Sox have used their return set to get on a roll.

Behind David Ortiz's first two-homer game since last summer, the Red Sox beat the Twins 12-5 on Saturday night, winning the first two games of the series and extending their winning streak to four.

Boston now has won more than three consecutive games for the first time since April 24-28, and the Red Sox have a chance to sweep the Twins on Sunday.

They earned that opportunity despite a laborious outing from Ryan Dempster, whose 127 pitches only got him through 4 2/3 innings. Dempster, who threw eight innings of shutout ball in his last trip to Target Field as a member of the Cubs last June, fought with his control all night, walking six batters and giving up eight hits.

It was the first time in Dempster's 16-year career that he'd thrown more than 125 pitches and failed to get out of the fifth inning, and he came an out short of being eligible to record a win off the Red Sox's offensive bounty.

The scoring started early off left-hander Scott Diamond, as Ortiz swatted a three-run homer in the first inning. Then, in the seventh inning, after the Twins had pulled within two runs, Ortiz ripped another homer to right-center off Anthony Swarzak, keying a four-run inning that put the game away.

Ortiz, who also had a RBI single and a walk, finished the night with six runs driven in. Dustin Pedroia reached base five times in six plate appearances, scoring three runs, Mike Napoli added three walks to a single, and Daniel Nava added a solo home run.

Craig Breslow, who threw 1 2/3 scoreless innings while the Red Sox were extending their lead in the sixth and seventh innings, was awarded the win.

Boston still was unable to pull back into a tie for first in the AL East after the Yankees beat Toronto, but the Red Sox should get right fielder Shane Victorino back on Sunday, and could also put shortstop Stephen Drew back in the lineup.

Those players, combined with an offense that found its groove on Saturday night, could help the Red Sox to a five-game winning streak before they head to Chicago for three games against the White Sox.