ATLANTA -- After his team played poorly the night before, Thrashers coach John Anderson challenged his players to focus on fundamental hockey.
"We weren't floundering in our zone as much because we played the body a lot more and helped out when the time was right," Anderson said. "Forwards were collapsing in front the net, all the little things that add up. I just thought our concerted effort was much better tonight."
Marty Reasoner set up both third-period goals to help Atlanta (7-6-1) snap a four-game home losing streak and two-game slide overall.
St. Louis earned a point for the third straight game, but is winless in five.
Ty Conklin stopped the first 27 shots he faced for St. Louis (5-6-4) before Enstrom scored to cut it to 2-1 with 7:01 left in regulation.
The Blues have lost their last two in shootouts, but coach Andy Murray didn't regret his decision to keep his team aggressive with a 2-0 lead.
"We didn't want to play shutdown in the third," Murray said. "We wanted to play attack oriented hockey. You don't sit on a lead. We made a mistake. They scored."
Atlanta began the game with a 25.5 percentage on the power play that ranked third in the NHL, but the Thrashers finished 0 for 6 after failing to score in two chances with an extra man Saturday in a 6-3 road loss to the New York Islanders.
Defenseman Zach Bogosian thought Atlanta was playing too passively in its end.
"We needed to get pucks on net and shoot more," Bogosian said. "We did that in the third."
Hainsey tied it with 3:31 to go. Reasoner won a faceoff near St. Louis' bench, and Hainsey, who controlled the puck at the left boards, beat Conklin with a wrist shot.
"You always hope that those bounces even out, and we were one shot in the Washington game," Reasoner said. "So we got even today. It's nice to catch that one break and put us in the right direction for these next home games."
Andy McDonald opened the scoring at 6:55 of the second period, and David Perron gave the Blues a two-goal lead on a power play at 7:08 of the third.
Johan Hedberg made 30 saves for Atlanta, while Conklin stopped 38 shots.
"Atlanta is a strong offensive team," Murray said. "The best way to play against them is to be in their zone. We had a couple of chances to make it 3-0 but we failed to execute.
In the tiebreaker, Peverley beat Conklin with a low shot. Kozlov scored after taking a wide turn from the right circle and crossing the slot.
"He's magic," Anderson said of Kozlov. "And the good thing about that is it's not the same one every time. I feel confident with (Hedberg) Slava in there because they practice it every day."
The Blues also lost a shootout 2-1 Saturday in Philadelphia. ... McDonald's goal ended a stretch of four straight games in which St. Louis failed to score in the first or second period. ... Atlanta improved to 5-6-1 against the Blues, 3-3-1 at Philips Arena.
Copyright by STATS LLC and The Associated Press
Arena: Philips Arena Location: Atlanta, Georgia
Referees: Chris Rooney, Bill McCreary Linesmen: Jay Sharrers, Mark Shewchyk
Attendance: 10,904 (58.8% full)
Team Stat Comparison
Power Play Goals
Power Play Opportunities
Shots on Goal
No scoring this period
Andy McDonald (5)
Assists: David Perron, Erik Johnson
David Perron (4)
(Power Play) Assists: Eric Brewer, Alex Pietrangelo