Galarraga and Avila exchanged words after Galarraga pitched scoreless first inning. The verbal altercation escalated enough that they had to be separated. Gerald Laird stepped between them.
Following the game, Galarraga called it a "misunderstanding," while outfielder Johnny Damon didn't seem too concerned.
"Dissension breeds winners," Damon said. "We should have done it earlier."
Galarraga (3-5) gave up four runs over five innings and struck out five in a no-decision.
Avila, who hit a ninth-inning, go-ahead two-run homer in Saturday night's win over the White Sox, was 2 for 5 on Sunday, including a double in the seventh inning.
Information from The Associated Press was used in this report.