Andrew Ladd and Anders Lee had scored for the Islanders in the third period to send the game into overtime, Lee's goal coming at the 19-minute mark. Tarasenko scored twice in the second period for the Blues, who were seemingly in control until Ladd scored for the home team at 13:04 of the third period to ruin Jake Allen's shutout bid.
Allen, who made 40 saves, denied Jordan Eberle and Anthony Beauvillier in the shootout. Tarasenko opened the scoring at 9:38 of the middle period after he spun past Leddy, then beat Thomas Greiss with a nifty backhand. Paul Statsny assisted.
Tarasenko increased the lead with a power-play goal at 15:34 of the second. The talented Russian forward whipped the puck past Greiss, finishing a passing play from Jaden Schwartz and Alex Pietrangelo for his third goal of the season.
The 25-year-old Tarasenko led the Blues with 39 goals and 75 points overall last season. St. Louis, which began with an opening-night overtime victory in Pittsburgh followed by a 4-2 home win over Dallas, improved to 7-1-2 in its past 10 games against the Islanders.
Allen, who had a career-best 33 wins last season, has won all three of his starts this season. The Islanders have lost two of their first three. Following the game, they departed for a three-game Western trip starting at Anaheim on Wednesday. They also will travel to San Jose and Los Angeles after which they return to play the Rangers at Madison Square Garden on Oct. 19.
Tarasenko's first goal of the game came shortly after the Islanders squandered a four-minute power-play opportunity earlier, more than a minute of which had them up two skaters. In the second, Blues defenseman Robert Bortuzzo was penalized four minutes for cross checking, an extra two minutes being assessed for pummeling Islanders forward Brock Nelson face down on the ice.
After Josh Ho-Sang was denied on a right pad save by Allen, Blues defenseman Carl Gunnarsson was assessed a slashing penalty, giving the Islanders a two-man advantage. But they failed to capitalize and were 0 for 6 overall on the power play.
Greiss was victimized for five goals in the Islanders' season-opening 5-0 loss at Columbus before he was replaced midway through by Jaroslav Halak, who earned the victory in the team's 6-3 home-opening win over the Buffalo Sabres.
NOTES: The Islanders visit the Blues on Nov. 11 to complete the season series . The Blues continued to be without injured forward Alex Steen and defenseman Jay Bouwmeester. ... Islanders forward Cal Clutterbuck missed his second straight game with a hip injury. ... Defensemen Dennis Seidenberg and Ryan Pulock were scratched by the Islanders.
UP NEXT Blues: At New York Rangers on Tuesday night. Islanders: At Anaheim on Wednesday night.