Gaudreau opened the week on Dec. 22 by recording a natural hat trick in a 4-3 come-from-behind victory over the Los Angeles Kings.
He followed that performance with two goals, including the game-winner, in a 4-1 win over Edmonton on Saturday.
The 21-year-old Salem, N.J., native ranks second among NHL rookies in goals (12), assists (17) and points (29) through 36 games this season.
Nashville centre Colin Wilson is the second star after putting up four goals and an assist in three games last week.
Arizona centre Sam Gagner scored two goals and four assists in three games to earn third-star honours.