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.
It is really special. I had a lot of friends and family here tonight, and for my first [NHL] game in here it was great. I played here as an elementary-school player in the city championships and this was my first time back. It was a lot of fun..
— Toronto native Brandon Pirri after scoring 2 goals for Panthers in win at Maple Leafs on Thursday