Baltimore won 8-2 and it's the 11th game covered by the Baseball-Reference Play Index Event Finder in which a team hit three home runs in one extra inning.
May 2, 1964 - Twins at Athletics
Harmon Killebrew put the Twins in front with a homer in the top of the ninth, but Kansas City tied things up on Rocky Colavito's RBI single. The 3-3 score held until the top of the 11th when Tony Oliva led off with a home run off Dan Pfister. The next batter, Bob Allison, took Pfister out as well, as did the next batter Jimmie Hall. The three consecutive homers spelled the end of Pfister's day, but Killebrew belted yet another off Vern Handrahan for back-to-back-to-back-to-back home runs. The A's went down quietly in the bottom half and lost 7-3. This is one of two games listed in which a team swatted four home runs in a single frame of bonus baseball, along with...
June 8, 1965 - Braves at Cubs
With one out and one on in the top of the 10th inning, Joe Torre knocked a two-run homer off Lindy McDaniel to give Milwaukee a 4-2 lead. Fellow future manager Felipe Alou followed suit for a back-to-back that knocked out McDaniel. Bob Hendley (the tough-luck loser in Sandy Koufax's perfect game later that year) came in for the Cubs. He walked Eddie Mathews and served up a two-run shot to Hank Aaron. Gene Oliver made it two sets of back-to-back homers with a long ball of his own that capped an 8-2 win.
May 16, 1969 - Pilots at Red Sox
One of the wildest games on our list. The short-lived Seattle Pilots scored six runs in the top of the 11th off Vicente Romo thanks to John Kennedy's two-run homer, Tommy Harper's solo dinger, Don Mincher's RBI double and Wayne Comer's two-run shot. Down 10-4, Boston stormed back in the bottom of the inning, scoring five times before John O'Donoghue put out the fire to secure a 10-9 victory.
August 7, 2001 - Giants at Reds
We wouldn't see another of these games for 32 years. Barry Bonds opened the top of the 11th with a homer off Danny Graves (#48 of 73 that year). The next three hitters, Jeff Kent, Andres Galarraga and Marvin Benard, went 3B-HR-HR to go up 7-3. San Francisco added two more in the inning for a blowout win.
May 31, 2002 - Royals at Rangers
I don't remember Hideki Irabu's final season in the Rangers bullpen, but he took a loss in this one on back-to-back-to-back home runs from Carlos Beltran, Mike Sweeney and Joe Randa.
September 8, 2002 - Mariners at Royals
K.C. was on the wrong end this time in a 16-9 loss. Seattle doubled their run total in an eight-run 11th inning off Blake Stein and Kris Wilson. John Olerud cracked a three-run homer and Stein then loaded the bases before departing. Ben Davis greeted Wilson with a grand slam and Mike Cameron added one right after for good measure. The Royals plated one in the bottom half to give them as many 16-9 defeats as the Chiefs.
September 29, 2006 - Royals at Tigers
The Tigers were tied with the Twins atop the A.L. Central with three games to play, although both teams were comfortably in playoff postition. Still, the 100-loss Royals swept this series in Detroit thanks in part to a comeback in this game. K.C. posted single tallies in the seventh, eighth and ninth innings to force extras. In the 11th off Jamie Walker, Emil Brown and Paul Phillips hit back-to-back jacks before Jeff Keppinger put the game out of reach with a two-run blast later on.
The Tigers were relegated to wild-card status, but despite not having home-field they beat the Yankees in the ALDS while the Twins lost to Oakland. Detroit swept the A's in the ALCS for their first pennant in 22 years.
June 21, 2010 - Reds at Athletics
Oakland's Kevin Kouzmanoff forced extra innings with home run off Francisco Cordero, but Cincy bounced back in the tenth when Ramon Hernandez took Michael Wuertz deep. Three batters later against Cedrick Bowers, Joey Votto and Scott Rolen hit consecutive dingers that provided needed insurance in a 6-4 win.
May 27, 2011 - Royals at Rangers
Texas was two outs away from a victory when Alex Gordon homered off Neftali Feliz to tie the game. The Royals completed the comeback in the 14th when Melky Cabrera and Eric Hosmer went back-to-back against Dave Bush and Brayan Pena piled on with a three-runner for a 12-7 win.
September 22, 2012 - Athletics at Yankees
The only game on the list in which the 3+ HR team lost. Jonny Gomes, Yoenis Cespedes and Chris Carter homered in the top of the 13th to give the A's a 9-5 lead. The Yankees scored four in the bottom half to extend the game, the last two coming on Raul Ibanez's heroics. New York walked off 10-9 in the 14th on a Brandon Moss error at first base. Fireworks start at the 0:50 mark below.
It's also worth mentioning three games in which a team went deep three times during extras, but not in the same inning.
April 29, 1951 - Red Sox at Athletics
Dom DiMaggio snapped a 6-6 tie with an 11th-inning homer, but Pete Suder's RBI single kept Philly alive. Tom Wright led off the 12th with a homer of his own, but the A's tied it again, this time on Eddie Joost's solo shot off Ellis Kinder. The third time would be the charm for Boston as they busted it open with four runs in the 13th off Johnny Kucab. The first four men all reached and scored, the last two thanks to a Ted Williams round-tripper. Mel Parnell closed it out for the Sox for a 12-8 win.
July 15, 1971 - Pirates vs. Padres
After a 1-1 pitching duel for 12 innings, Ivan Murrell's pinch-hit homer pushed the visiting Padres in front. Willie Stargell saved the Bucs in the bottom of the 13th with a two-out blast off Al Severinsen. The game rolled into the 16th and although San Diego took the lead when Don Mason scored on Jim Nelson's wild pitch, the Pirates came back again. Richie Hebner homered off Danny Coombs to tie the game before Roberto Clemente rocked a walk-off in the 17th. This is one of two times that the home team hit three in extras.
August 20, 2001 - Reds vs. Cardinals
Here's the other. Ken Griffey Jr. sent this one to the tenth with a last-gasp RBI single off Mike Timlin. St. Louis scored twice against Danny Graves in the away half of that tenth inning, but the Reds tied it with one-out back-to-back home runs off Andy Benes by Todd Walker and Kelly Stinnett. An inning later, Griffey ended the game in memorable fashion.