The Ducks led 9-0 in shots less than six minutes into the game, but the Canadiens then scored three times on seven attempts to chase starter Ryan Miller at 10:13 in favor of Reto Berra, who was called up on Friday to replace the injured John Gibson.
Shaw, who was claimed on waivers from Anaheim on Jan. 15, scored his first as a Canadien at 6:16 when he banged in a Byron Froese pass from the edge of the crease. Two minutes later, Morrow added one on a power play on a one-timer of Victor Mete's pass from the right point.