Beckett (2-2) allowed two runs and five hits and Mike Aviles went 4 for 5 with a homer and two RBIs for the Red Sox, who had no trouble with this big lead after squandering a nine-run advantage in a loss to the New York Yankees on Saturday.
Beckett jawed with home plate umpire Adrian Johnson after a rough first inning, but the fiery Texan finished his evening by striking out the side in the sixth.
Nick Blackburn (0-2) gave up five runs and eight hits in just three innings for the Twins.
Beckett had a heck of a time in the first inning, needing 37 pitches to grind through it. He walked three straight hitters, including Justin Morneau with the bases loaded, to make it 3-1.
Beckett gave several long looks into Johnson on a couple of close pitches to Josh Willingham and Danny Valencia. After getting Valencia to ground out to end the inning, Beckett let out a scream as he walked off the mound and yelled "That's (expletive) five outs!" in Johnson's direction. As Johnson started to walk toward Beckett, manager Bobby Valentine briefly left the dugout to diffuse the situation.
The only trouble Beckett gave the rest of the way was to the Twins offense. Willingham doubled home Jamey Carroll in the fifth, but that was all Minnesota could muster.
Ortiz's monster, two-run shot in the third inning landed on the stairway in right field — an estimated 429 feet — to make it 5-1. It was the continuation of an incredible start for the 36-year-old slugger, who is hitting .444 with three homers and 15 RBIs. His 28 hits are a career-high for April.
Adrian Gonzalez had three hits and two RBIs and Scott Atchison and Matt Albers pitched three innings of scoreless relief.
The Red Sox led the Yankees 9-0 after five innings on Saturday, but their beleaguered bullpen gave it all back and then some, including consecutive seven-run frames in a loss that Valentine termed rock bottom. They have rebounded with two strong performances in Minnesota, which has lost four straight and is sinking plenty fast itself.
Blackburn left his previous start in the sixth inning with stiffness in his right shoulder and was skipped the next time through the rotation. He gave up three runs and five hits in the first and needed 71 pitches to get through three innings.
Left-hander Matt Maloney didn't fare any better, getting tagged for five runs and eight hits in 1 2-3 innings.
Willingham had two hits and an RBI for Minnesota.
NOTES: OF Carl Crawford flew from Ft. Myers, Fla., to Boston for an examination on his strained left elbow. Valentine said they were "still gathering information" but said it would remain a concern until he was deemed 100 percent. Crawford has yet to play this season. ... The Twins placed INF Tsuyoshi Nishioka on the minor league DL with a high ankle sprain. GM Terry Ryan said Nishioka could miss 10 days with the injury. ... The Twins planned to call up OF Ben Revere from Triple-A Rochester on Wednesday to replace Willingham, who is taking three days of paternity leave while his wife has the couple's third child. ... The Red Sox will send struggling RHP Clay Buchholz (1-1, 9.00 ERA) to the mound to go for the series sweep against Minnesota's RHP Liam Hendriks (0-0, 3.86 ERA) on Wednesday. Buchholz gave up six earned runs and five home runs in a loss to the Yankees last week.
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