Brian Dozier got the Twins' first hit off Moore when he lined a double with two outs in the sixth down the left-field line. Dozier then scored to tie it at 1 on Jamey Carroll's run-scoring single.
The highlight for Minnesota was the major league debut of right-hander Michael Tonkin, who came in with two men on base and struck out Longoria to end the seventh.
"It's the kind of situation you want to be in, I guess," the 23-year-old Tonkin said. "You want the tough ones. It was pretty cool for the first guy I faced to be Longoria. That's kind of exciting, a little memorable."
The series was not one most of the Twins will choose to remember.
"We're all in here to win and we haven't been doing that," Pelfrey said. "We have to find a way to keep it loose in here and continue to have fun. It's tough when you're not doing it, but if we don't find a way, this long season will get a lot longer."
A number of regulars, including Tampa Bay's Ben Zobrist, Desmond Jennings and Yunel Escobar, along with Minnesota's Justin Morneau and Ryan Doumit, were not in the starting lineup. The Twins loss followed another 4-3 decision for Tampa Bay in 13 innings that ended just 12 hours earlier.
Zobrist hit an RBI single with two outs in the 13th to win it. He lined a 1-2 pitch from Ryan Pressly (2-1) into the gap in right-center field, ending a 4-hour, 47-minute game that featured 35 strikeouts — 19 for Rays pitchers.
Cesar Ramos (2-2) got two outs, escaping a jam with runners at first and third in the 13th to get the win.
NOTES: The Twins have been swept five times this season in series of three games or more. They have lost nine straight against the Rays. ... Rays RHP Alex Cobb, struck in the right ear by a liner hit by Kansas City's Eric Hosmer on June 15, underwent a concussion test Wednesday and feels the results will be positive. He could throw batting practice for the first since getting hurt Sunday. ... The Twins placed LHP Caleb Thielbar on the bereavement list and recalled Tonkin from Triple-A Rochester. It was announced Tuesday that Thielbar would be leaving the team following the death of his grandmother.