Stempniak had an open shot from the left circle off a pass from Eric Brewer and beat Rick DiPietro to the far corner to give the Blues their sixth win in seven games (6-1-0).
The Islanders were cruising to a 2-0 victory with less than three minutes left in the game when Jay McClement and Petr Cajanek scored in a 38-second span to force overtime. Curtis Sanford picked up the win by stopping 25 shots.
Smyth, acquired from Edmonton on Tuesday, assisted on Mike Sillinger's first-period goal, and played a key role in Marc-Andre Bergeron's second-period goal. After the goal was knocked off its moorings, Smyth used his skate to put it back in place just before Bergeron's shot deflected in.
DiPietro wound up stopping 36 shots.
The overtime point leaves the Islanders in sole possession of seventh place in the Eastern Conference, one point behind Atlanta and one point ahead of Montreal.
St. Louis outplayed the Islanders in the first period and had a golden chance to score the first goal, when a shot left the puck laying on the goal line, but defenceman Brendan Witt swept it out of the goal mouth.
Smyth, who earned a warm welcome from the crowd of 12,263, assisted on the opening goal by Sillinger at 10:16. Down the left side, he centred a pass to Sillinger, who faked Sanford down with a forehand move and tucked a backhand into the open net.
Bergeron gave New York a 2-0 lead 40 seconds into the second period when he stuffed Jason Blake's pass past Sanford.
St. Louis tied the game late in the final period with a pair of goals 38 seconds apart.
McClement broke DiPietro's shutout bid at 17:29 off a scramble with a wrist shot from in front.
Cajanek tied the game at 18:07 on a wrist shot from the left circle.
Notes: DiPietro set a career high with his 13th straight start. ... When Mike Kitchen coached the Blues from the start of the season, the collective plus-minus total of the team was -96. Since Andy Murray took over, the team, the roster is a plus-50. ... The Blues entered the game with a 4-1-1 record against the Eastern Conference. ... Smyth becomes the first Islander to ever wear No. 94.