Heading into Saturday's game, the club had lost 129-man games this season. Rookie Ryan Nugent-Hopkins is likely to miss the next month with a separated shoulder, while blueliners Tom Gilbert and Ryan Whitney are both dealing with lower-body injuries.
"They've been weird injuries and it's been like that ever since I got here to be honest," winger Taylor Hall told the Sun. "Those are tough to take.
"We need those guys back as soon as possible, but in the meantime we're going to have to make do without and play as hard as we can."
In 41 games with the Oilers, Eberle has tallied 17 goals and 26 assists for 43 points.
Meanwhile, center Anton Lander was blindsided by Stars forward Steve Ott with a shoulder to the head, but didn't appear to show any ill effects from the headshot.
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