The Blue Jays set a club record with their 10th consecutive win, while the Orioles lost their ninth straight, the club's longest losing streak in five years.
Toronto has won 13 of its last 14 games but almost gave this one away after taking a 5-0 lead through six innings.
It was the Orioles, however, who gave the game away when a soft pop fly fell between three Baltimore players in the eighth inning, allowing the winning run to score.
"We almost let this one get away," Toronto's Willie Upshaw said. "We are playing hard and we just keep battling. . . . We really aren't thinking about the streak. I didn't even know about the record."
In the Blue Jays' eighth, Garth Iorg singled off Baltimore starter Mike Boddicker (5-3) with two outs, then Tony Fernandez lofted a high pop to shallow left field. The ball fell between left fielder Alan Wiggins, third baseman Ray Knight and shortstop Cal Ripken.
Mark Eichhorn (8-2), who entered in the sixth, earned the victory. His eight victories are the most by a relief pitcher in the major leagues this season. Jeff Musselman pitched the final two innings for his second save.
Toronto led, 5-0, after six innings, but Baltimore rallied to tie the game with five runs in the seventh.
Minnesota 5-7, Chicago 2-4--Frank Viola allowed four hits over seven innings in the opener, and Dan Gladden hit a two-run single to cap a four-run second inning in the second game as the Twins swept the White Sox in Chicago.
In the first game, Viola (5-5) struck out two and walked none before yielding to George Frazier in the eighth, when Chicago scored its runs. Roy Smalley hit a three-run homer for the Twins in the sixth inning.
In the nightcap, Twins reliever Juan Berenguer (4-0) pitched 3 innings, giving up four hits and no runs. Keith Atherton pitched 1 innings to earn his second save.
New York 8, Milwaukee 3--Dennis Rasmussen, threatened with banishment to the minors by owner George Steinbrenner after a string of bad outings, held the Brewers hitless for 6 innings in New York as the Yankees snapped a three-game losing streak.
Rasmussen's bid for a no-hitter ended when Jim Paciorek hit a trickler that grazed the third base bag for a single in the seventh. Rasmussen allowed three hits and two runs in 7 innings.
With Steinbrenner watching from his private box, Rasmussen (4-4) retired the first 12 Milwaukee batters and breezed until Paciorek's single. Rasmussen left the game after solid one-out singles by Rick Manning and Dale Sveum and a walk to Mike Felder loaded the bases in the eighth.
Mark Salas, Ron Kittle and Henry Cotto homered for the Yankees, who won for the first time since being swept in a three-game series by Toronto and falling into second place in the American League East.
With the score tied 4-4, Lou Whitaker started the Detroit seventh with a single, Bill Madlock had a sacrifice bunt and Kirk Gibson was given an intentional walk.
Trammell then hit the first pitch into the lower deck in left field for his seventh home run, knocking out Clemens (4-6). Clemens, the 1986 American League Cy Young Award winner, gave up seven runs on eight hits, struck out four and walked two.
Detroit's Frank Tanana (5-3) allowed seven hits, walked five and struck out five.
Stewart (7-6) walked three and struck out nine as Oakland won its fourth straight game.
Texas starter Greg Harris dropped to 2-5.
Jackson hit his sixth homer of the season and the 43rd of his career against Texas after reliever Mike Loynd walked Carney Lansford with one out in the fifth to make it 6-1.
Cleveland 10, Seattle 6--Joe Carter's two-run homer highlighted a five-run sixth inning as the Indians beat the Mariners in Seattle.
Former Mariner Mark Huismann (1-3) pitched four scoreless innings of relief for the win. Reliever Mike Trujillo (2-4) took the loss for the Mariners, allowing two runs on one hit.