Boston allowed late goals in each period -- including the tying score with 68 seconds left in regulation -- and settled for a 3-3 tie against visiting Phoenix on Sunday.
Travis Green scored one goal and set up another for the Bruins, winless in a season-high four straight (0-2-1-1) after winning five of six.
"It's been tough," left wing Sergei Samsonov said. "It's frustrating. We've got to capitalize on those last couple of minutes, get our 2 points, and get out of there. It's probably more mental than anything."
Boston's power play continued to struggle Sunday, going scoreless on five opportunities while giving up a shorthanded goal. The Bruins are 1-for-17 with the man-advantage in the last four games.
"There's a fine line between winning and losing," Boston coach Mike Sullivan said. "Short lapses cost us at crucial times."
Alternating between veteran goalie Felix Potvin and 23-year-old Andrew Raycroft has worked well this season for the Bruins, but Raycroft is making a strong case for more playing time. While Potvin has allowed 12 goals in his last three games, Raycroft has surrendered 12 while winning four of his last six starts.
Despite Kovalchuk's league-leading 18th goal, Atlanta was a 4-3 loser to last-place Pittsburgh on Sunday.
The Thrashers have lost three of four following a franchise-record four-game win streak.
"We threw those two points away," Atlanta coach Bob Hartley said. "We got outworked. It's very simple; we were not ready. Three-quarters of our team has never been a part of the playoffs, so you shouldn't let down. You should be waking up and looking at the standings every morning."
Kovalchuk's goal was his sixth in the last eight games, giving him 10 points in that span. He is fourth in the NHL with 30 points and tops the league with 11 power-play goals and 120 shots on goal.
Kovalchuk has eight goals and 11 points in nine career games against Boston.