ST. PETERSBURG, Fla. -- Brandon Inge still has some pop in his bat.
"The last two years I wouldn't have had situations like that," Inge said. "It's getting back to where I'm seeing guys on ahead of me and it feels like I'm getting back to my old self."
Tampa Bay dropped its second straight, falling to 13-3 at home, and failed again to become the first major league team to reach 20 wins.
The 34-year-old Inge, dumped by Detroit on April 26 after 11 seasons with the Tigers, hit a three-run shot off Moore (1-2) in the third inning to give the A's a 5-4 lead after Tommy Milone struggled in the first.
"That home run was huge. It felt like a 10-run homer," Oakland manager Bob Melvin said. "To be down and then take the lead with that homer -- it was probably the biggest hit we had on the trip."
The A's wrapped up a 5-4 East Coast road trip against Baltimore, Boston and Tampa Bay, winning series against the Red Sox and Rays.
"A three-team swing can be a little taxing," Melvin said, "but it was an above .500 road trip and we'll take it."
Inge, an All-Star in 2009 when he had 84 RBIs, added a sacrifice fly in the seventh for his first game with at least four RBIs since July 5, 2010, against Minnesota. The third baseman was 1 for 10 with four strikeouts in the two previous games.
"A lot of what he does doesn't really show up statistically," Melvin said. "Whether it's grinding out at-bats or in the field, we're glad to have him."
"It was surprising that I threw that many pitches in the first," Milone said. "I just went back to trying to throw strikes and that settled me in."
Upton has 11 RBIs in 14 games since being activated from the disabled list on April 20. He also drew three of the seven walks issued by A's pitchers, while the Rays left eight runners on base.
Milone has given up 12 runs in his past two starts, including seven to Boston last Monday.
Cook has not allowed a run in 14 2/3 relief innings.
"It was really contributions from everyone across the board," Melvin said. "Really, we needed contributions with extra layers to get this game, and the guys stepped up."
Moore gave up a career-high eight runs in 4 2/3 innings and struck out four. He struggled to get through a five-run third by the A's that included RBI singles by Gomes and Cuban rookie Yoenis Cespedes.
"He just got out of whack," Rays manager Joe Maddon said. "He couldn't throw a strike where he wanted to with the fastball. He has a great fastball, he just doesn't know where it's going all the time quite yet. I've seen that before with our other young pitchers, so he's going to be fine."
Gomes added an RBI double and Barton bought in two more in a three-run fifth that knocked Moore out of the game after 105 pitches.
Gomes hit a go-ahead homer in extra innings Saturday and went 5 for 9 with four RBIs, two walks and two strikeouts in the series against the team that drafted him in the 18th round in 2001.
Tampa Bay pitchers gave up season highs in runs and hits (10).
Rays LF Desmond Jennings left in the third with a sore left knee. He went 0 for 1 with a walk, a run scored and a stolen base. ... The Rays recalled LHP Cesar Ramos before the game after they optioned RHP Brandon Gomes to Triple-A Durham late Saturday night. Ramos gives the Rays three left-handers in their bullpen, joining J.P. Howell and Jake McGee. ... Ramos pitched a perfect ninth inning. He held left-handed hitters to 0 for 19 at Durham. ... Monday is the Rays' last off day until May 23. ... Inge has 141 career home runs. ... A's manager Bob Melvin announced that Jarrod Parker and Brandon McCarthy have been switched in the rotation, with McCarthy starting Tuesday and Parker on Wednesday against Toronto. .... Oakland 2B Jemile Weeks was given the day off to rest the slight tightness in his groin. .... It was the sixth day game for the A's, the fewest in the majors. .... Attendance was 23,873.