McDonald fired a wrist shot into the net in the first round of the shootout and Boyes scored on the Blues' second try to nail down the win.
"It was a big win for us," McDonald said. "We have wanted to be a little bit more solid in closing games out, but we've played well the last two games on the road and hope it will continue at home."
Alex Frolov, Brad Richardson and Scott Parse had goals for Los Angeles. Jarret Stoll notched a goal and an assist. Jonathan Quick made 27 saves.
Both teams scored two goals in the third period to force the overtime. Kariya scored with 2:20 left in regulation to put St. Louis in the lead, but Frolov tied the score 4-4 with 25 seconds to play after Quick had been pulled for a sixth attacker.