The win put the defending Stanley Cup champions on the verge of surviving the first round, leading 3-2 heading to Game 6 in Los Angeles on Saturday.
Alex Pietrangelo scored on a wrist shot from the point with 44.1 seconds remaining in regulation and goalie Brian Elliott off for an extra attacker. That forced overtime for the second time in the series.
The Kings' Justin Williams scored in the final minute of Game 1, also in St. Louis.
Jeff Carter scored in the opening minute of the second and third periods for the Kings, who became the first road team to win in the series.
That group is not satisfied until we win a Stanley Cup. When we do win that Stanley Cup, I don't think we'll be satisfied then either. We're going to want another one. We have the group to do it. We have all the pieces. We just need to put them together.
— Ducks forward Ryan Kesler after signing a six-year extension with Anaheim this past July