BALTIMORE -- The Baltimore Orioles have too much else going on to be overly excited about ending their miserable run of 14 consecutive losing seasons.

Manny Machado blooped an RBI single that eluded left fielder Matt Joyce's desperate dive with two outs in the 14th inning, and Baltimore beat Tampa Bay 3-2 Thursday to complete a three-game sweep and remain atop the AL East.

With their 81st victory -- and 13th in a row in extra innings -- the Orioles are assured no worse than a .500 record for the first time since 1997.

"There's a bigger goal in mind," manager Buck Showalter said. "That wasn't the goal from Day One this spring. Really, Day One of the offseason. It's watching other teams for years and saying, 'We want to do what they're doing.' We'd like to get a chair at the dance, you know?"

It's been an incredible season for the Orioles, who finished in the cellar in each of the previous four years. Baltimore (81-62) remained in a first-place tie with the New York Yankees, who beat Boston on Thursday night, 2-0.

After briefly celebrating a victory that capped a 5-2 homestand against the Yankees and Rays, the Orioles packed in the clubhouse for a trip to Oakland.

"It makes that West Coast trip a little easier when you win," said closer Jim Johnson, part of a bullpen that kept Tampa Bay scoreless on four hits over the final 6 2/3 innings. "You can enjoy it for a little bit, the five hours you're on the flight, but that's about it."

The Rays fell four games back in the division by virtue of yet another one-run defeat punctuated by a lack of offensive punch. Tampa has lost 13 of its last 16 one-run games, including a 3-2 decision Wednesday night.

"It's just the same old story: We can't score enough runs," manager Joe Maddon said. "We pitched extremely well, we played well in the field overall, loved the effort."

But the Rays stranded 10 and went 1 for 7 with runners with scoring position. Tampa Bay left Camden Yards for Yankee Stadium to play a three-game series that begins Friday night.

Sixteen pitchers took part in the game, which lasted 5 hours, 14 minutes. Tampa Bay used a club-record 26 players, including nine pitchers.

After the Orioles squandered a bases-loaded, no-out threat in the 13th, Chris Archer (0-3) got the first two outs in the 14th before Adam Jones walked and Endy Chavez singled. Machado followed with a soft liner toward the line that Joyce trapped.

"I know it hit my glove on the bottom," Joyce said. "It was hard to tell what exactly happened. Only thing I can tell you is I didn't come up with it."

Machado, a 20-year-old rookie, scored the game-winning run in the bottom of the ninth Wednesday night.

"I'm having a blast," Machado said. "This team is great to be around. It's a great group of guys. We're all excited. We're all having one goal, which is make the playoffs."

The Orioles' success in extras this season matches the longest in the majors since Cleveland won 13 straight extra-inning games in 1995.

Randy Wolf (2-0) earned the win by striking out Joyce with two on in the top of the 14th. Baltimore has won 14 of 19 overall and is 26-11 since Aug. 3.

Although the Orioles blew a 2-1 lead in the eighth inning, they improved to 64-0 when leading after the seventh.

Baltimore loaded the bases with no outs in the 13th but could not score after the Rays employed five infielders in hopes of cutting off the potential winning run at the plate. Robert Andino hit into a force at home, pinch-hitter Matt Wieters struck out and Nate McLouth struck out.

"We came up short that inning," Machado said, "but we won it in the next."

Orioles rookie Wei-Yin Chen gave up two runs and eight hits in 7 1/3 innings. Working with a 2-1 lead in the eighth, Chen walked leadoff hitter Desmond Jennings, who advanced on a passed ball and a stolen base before scoring on a slow roller to third by Ben Zobrist for a hit.

In the bottom half, the Orioles got runners on the corners with one out before Joel Peralta struck out Machado and Mark Reynolds.

Limited to four hits through the first six innings, Baltimore went ahead with a two-run seventh. After Rays reliever Wade Davis mishandled a bunt by Machado, Andino walked and seldom-used backup catcher Taylor Teagarden hit a two-run double into the gap in right-center.

Tampa Bay starter Jeremy Hellickson allowed four hits and three walks in five-plus innings. He was pulled after J.J. Hardy led off the sixth with a single.

Jake McGee, who struck out all four batters he faced on Wednesday night, came in and struck out pinch-hitter Lew Ford, Jones and Chris Davis. It was McGee's 18th consecutive scoreless appearance since July 18.

To that point, the game's only run came in the fourth inning. Singles by Zobrist and Evan Longoria put runners at the corners before Jeff Keppinger hit a sinking liner to center. Jones made a fine diving catch, and Zobrist tagged up from third and scored.

Game notes

An MRI on Baltimore RHP Jason Hammel showed no new damage to his right knee, and he hopes to return soon. "It's probably the best situation we could have," he said. ... Jennings returned to the Tampa Bay lineup after missing four games with back tightness. ... Tampa Bay 2B Ryan Roberts fouled a ball off his left ankle in the 11th and left the game. X-rays were negative. ... David Price (17-5, 2.54 ERA) will start Friday night for Tampa Bay against CC Sabathia (13-5, 3.56) . ... Baltimore has held the Rays to 10 runs in the last seven games between the teams. ... Right-hander batters are 9 for 93 (.097) against McGee. ... TB's B.J. Upton went 0 for 6 and was 1 for 14 in the series.