Dmitrij Jaskin scored twice for St. Louis and Jaden Schwarz had the other goal for the Blues, who missed both attempts in the shootout.
Both teams held out most of their star players.
Jaskin had a wraparound goal in the first period and was also alone on his second goal at 1:52 of the second period.
The Blues forward threw a seemingly harmless shot at the goal from just inside the boards that Lightning goalie Cedrick Desjardins let sail over his shoulder for a 2-0 Blues lead.
Kristers Gudlevskis replaced DesJardins in the middle of the period and allowed a goal to Schwartz on the first shot he faced to make it 3-0.
Erne deflected a shot from Mark Barberio late in the second period to cut the deficit to 3-1.
Erne struck again 1:31 into the third period, scoring from right in front of the net after a centering pass from Brown.
Pyatt tied the game with a sharply-angled shot from the left wing that surprised Blues goalie Brian Elliott.