Detroit's Jeremy Bonderman hit Brett Gardner in the leg with his first pitch and umpire crew chief Eric Cooper warned the benches against further trouble.
Gardner's hard slide into second base at the end of Monday's game took out Carlos Guillen, who went on the disabled list with a bruised knee. One out after the speedy Gardner was hit, Teixeira made it 2-0.
The warnings, however, didn't seem to end the hostilities.
With the Yankees leading 9-4, reliever Chad Gaudin hit Cabrera, his first batter, in the back to start the eighth. Tigers manager Jim Leyland came out to argue when Gaudin wasn't ejected or warned.
After the half-inning, Leyland came out again and was immediately ejected.
Detroit reliever Enrique Gonzalez threw behind Derek Jeter with one out in the bottom of the eighth, but nothing happened and Jeter later walked. Gonzalez later came inside to Teixeira and Robinson Cano, getting a glare from the latter.
Cano and Curtis Granderson also homered for the Yankees, who remains tied with the Tampa Bay Rays atop the AL East.
Moseley (3-2) went five innings, allowing four runs and five hits. He also gave up a two-run homer to Don Kelly.
Six of the seven runs that Bonderman (6-9) allowed in five innings were earned.
Cano's homer followed Teixeira's shot. The Yankees also got an RBI triple from Ramiro Pena, who was in the lineup as Alex Rodriguez sat out for the second night in a row after hurting his calf Monday.
Austin Kearns doubled with the bases loaded in the Yankees seventh.
The Yankees got help from Detroit during a three-run fourth that made it 6-2.
Gardner was on second when Teixeira hit a hard hopper that Cabrera couldn't handle at first base. Second baseman Ramon Santiago came over and threw to first from almost directly behind the bag, though Teixeira was the only person there. The ball skipped toward the backstop and catcher Alex Avila couldn't corral it, allowing Gardner to score. Cabrera and Santiago were charged with errors.
Kerry Wood worked out of a jam in the seventh, striking out Santiago and Ryan Raburn with the bases loaded and Cabrera on deck, after coming in and giving up a single to Austin Jackson.
NOTES
Teixeira had been 1-for-15 against Bonderman before Wednesday night. … Just at twilight, Teixeira hit a high fly ball to right that Raburn lost in the sky, throwing out his arms as if to say "where'd it go?" before he recovered, but not in time to stop the ball from bouncing off the warning track behind him and over the fence for a ground-rule double. … Shortly before sunset, a vivid rainbow appeared over the Bronx, behind left-center field. … The teams combined for six homers, all in the first five innings. The Yankees and Red Sox combined for seven homers on May 17.