The penalties come as a result of separate incidents in a game between the two teams at Madison Square Garden on Saturday night.
Orr was suspended for a cross-checking Capitals star Alexander Ovechkin late in the third period of the game. He will forfeit US$13,235.29 in salary and won't be eligible to return until Jan. 13 against Boston.
"(Orr's) actions with his stick were reckless and dangerous," said Colin Campbell, the NHL's senior executive vice-president of hockey operations. "Although no injury resulted, the action is unacceptable."
Brashear received his suspension after being given a match penalty for punching Rangers defenceman Aaron Ward. He gives up $12,195.12 and can return Jan. 4 against Montreal.
The money goes to the Players' Emergency Assistance Fund.