TAMPA, Fla. -- The Detroit Red Wings latest milestone game had a disheartening outcome.
"We didn't have everybody being good enough here tonight in my opinion," Red Wings coach Mike Babcock said. "I felt we could have found a way to be better."
Killorn beat Jimmy Howard from just outside the crease to give the Lightning a 3-2 lead with 3:11 to play. Palat added an empty-net goal with 63 seconds left.
"I just felt that they competed harder around the front of the net at the end of the game," Babcock said. "We didn't compete hard enough around the front of the net, and that's defensively, offensively. You can't have guys be more determined than you."
Tampa Bay also got a goal from Tom Pyatt. The Lightning, who had lost four of five, are second in the Atlantic Division, one-point ahead of Montreal and Toronto.
"For everybody, it was a little bit of a cloud was lifted," Tampa Bay coach Jon Cooper said. "I know it's one game, but the taste of winning lasts for two weeks, and that's a good taste to have."
Detroit, which has battled injuries to key players this season, entered on a 6-2-2 stretch. The Red Wings, 0-2-2 against Tampa Bay this season, trails the Lightning by seven points.
"We feel pretty good about ourselves," Red Wings defenseman Jonathan Ericsson said. "Would have been feeling way better if we came out with a win."
The Red Wings went ahead 2-1 on Jurco's nifty backhander at 11:19 of the second. The rookie stopped a 14-game goal drought.
Pyatt got his first goal in 18 games, dating to back to April 4, when he got a backhander past Howard that pulled the Lightning even at 2 with 2:46 left in the second.
Alfredsson put the Red Wings up 1-0 from the low right circle off a pass from Pavel Datsyuk 17:18 into the first. The goal gave Alfredsson 1,143 NHL points, which moved him Nicklas Lidstrom to become the second-highest scoring player from Sweden. Mats Sundin tops the list with 1,349.
Datsyuk got his 800th point on Alfredsson's goal.
Palat tied it at 1 with a rebound power-play goal 1:44 into the second. Tampa Bay had failed to score with the man advantage in its previous seven games.
This was the final game for both teams before the Olympic break, which could help the Lightning, who are without injured centers Steven Stamkos (broken leg) and Valtteri Filppula (broken ankle). Goalie Ben Bishop, who left Thursday night's game with Toronto after the second period due to an upper body injury, made 31 saves.
"A win before the break puts everybody in a good mood," Bishop said.
Howard stopped 24 shots.
It was 17 years ago Saturday that Chicago senior adviser Scotty Bowman won his 1,000th NHL regular-season game as a coach when the Red Wings beat Pittsburgh 6-5 in overtime. Bowman, a regular at Lightning home games, had right knee replacement surgery on Jan. 24 and is rehabbing the knee at his Florida home. ... Alfredsson has 27 goals and 72 points in 63 games against the Lightning. ... Tampa Bay reassigned D Jean-Philippe Cote to Syracuse of the AHL. ... Red Wings D Niklas Kronwell was minus-3.