Andrew MacDonald added two goals for New York, which has won two straight after dropping four in a row. Michael Grabner finished with a goal and an assist in the victory, while Al Montoya made 21 saves.
Chris Stewart and Andy McDonald scored for St. Louis, which has lost four straight and seven of its last eight. Ben Bishop stopped just 17 shots in defeat.
The Islanders had a golden opportunity to grab the early edge. Just five minutes into the contest Bishop ventured out of the net in an attempt to reach a loose puck, but was easily beaten to the disc by Parenteau, who inexplicably missed a wide open net from the right wing.
Parenteau then set up Tavares for his 24th goal of the season and a 1-0 lead. Tavares took a feed from Parenteau in the high slot and simply stick-handled his way through three St. Louis defenders before slipping a backhander past Bishop at the 9:12 mark.
A turnover in the neutral zone led to a Parenteau goal in the final minute of the period for a 2-0 edge. Tavares picked up the puck at the center red line and sent Grabner into the St. Louis zone along the left wing. The Islander rookie fired a pass from the left circle toward the front of the net for a streaking Parenteau, who neatly redirected the puck home for his 15th goal.
MacDonald rifled a point shot into the back of the net at 12:49 of the second period to extend the Islander lead to three, before the Blues finally woke up in the third.
St. Louis seemed to sleepwalk through the first 40 minutes, then finally beat Montoya at 3:26 of the third when McDonald took a pass from T.J. Oshie and snapped a shot home from the left circle.
The Islanders quickly countered when MacDonald raced in on a breakaway just under three minutes later and beat Bishop with a high shot from the left circle for a 4-1 advantage.
St. Louis cashed in a power play with 9:42 left to again pull within two as Stewart banged in a rebound for his 20th goal of the season, but the Islanders again had an answer just over two minutes later.
After Montoya stopped McDonald from in close, New York went the other way. Grabner walked around St. Louis defenseman Alex Pietrangelo in the left circle and beat Bishop high for his 26th goal of the campaign.
Tavares has matched his goal total from last season…Grabner halted an eight- game goal drought…Stewart has seven goals in nine games since being acquired by the Blues in a trade with Colorado…The Blues were 1-for-3 on the power play and killed off each of the Islanders’ three chances with the extra skater…St. Louis fell to 10-4-3 against the Eastern Conference, including 4-2-0 against the Atlantic Division.