Pelfrey, who rejoined the Twins on a two-year, $11 million deal this offseason, gave up two runs on three hits with two strikeouts in his second Grapefruit League outing.
"The biggest thing tonight was I didn't throw enough strikes," Pelfrey said. "I was kind of all over the place. But it's still early. And physically, I felt good."
Right-hander Chris Tillman, Baltimore's likely Opening Day starter, was also unable to get through three frames, giving up three runs (one earned) on four hits over 2 1/3 innings.
The Twins scored three runs in the second inning, aided by an error by Paul, who allowed Josh Willingham to advance to third base on a dropped flyball. Trevor Plouffe brought home Willingham with an infield single for the game's first run before Kurt Suzuki and Alex Presley added RBI singles of their own.
The Orioles also scored in the fourth against Twins closer Glen Perkins, who loaded the bases with one out and surrendered a run on a groundout from Jemile Weeks.
Baltimore broke it open with five runs in the sixth inning against left-hander Scott Diamond, but only one run was earned because of a throwing error by second baseman Jorge Polanco. After the run-scoring throwing error, Paul added an RBI groundout before Steve Pearce connected on a two-run double.
Orioles left-hander Zach Britton, who is competing for the fifth spot in Baltimore's rotation, threw two scoreless innings with two strikeouts. He took a ball off his right wrist on the final play of the fifth, though manager Buck Showalter said after the game he expected him to be fine.
The Twins scored twice in the seventh against right-hander Steve Johnson, as Eduardo Escobar laced an RBI triple and scored on a sacrifice fly from Kennys Vargas.
Up next for Orioles: Miguel Gonzalez will take the mound for the Orioles on Thursday afternoon against the Rays in his second spring start. Ace David Price will counter in the 1:05 p.m. ET matchup at Ed Smith Stadium.
Rhett Bollinger is a reporter for MLB.com. Read his blog, Bollinger Beat, and follow him on Twitter @RhettBollinger. This story was not subject to the approval of Major League Baseball or its clubs.