Henrik Lundqvist made 27 saves for the Rangers, who have lost two in a row in regulation after recording at least one point in 13 consecutive games (10-0-3). New York, third in the Atlantic Division, dropped seven points behind New Jersey, which beat Colorado 4-2.
"We give an effort like this, this is what happens," Rangers center Scott Gomez said. "Everyone should be pretty upset with themselves, but in saying that, we know what type of team we are. We can't dwell on this."
The Rangers are sixth in the Eastern Conference but only four points ahead of ninth-place Buffalo, the first team below the postseason cutoff. New York lost 3-2 at Florida on Friday.
"It's very disappointing," Lundqvist said. "We came on this trip with a lot of confidence, and we felt like our game was where it should be. But it felt like we were missing a little bit of intensity in our game and got outbattled a little bit."
Smith, acquired from Dallas on Feb. 26, has three shutouts in 29 games this season. The first two came with the Stars.
Picard put the Lightning ahead 1-0 on a rebound goal with 46.2 seconds left in the second period. Jeff Halpern assisted on the goal, giving him four assists and seven points during a four-game point streak.
St. Louis made it 2-0 with a power-play rebound goal at 6:40 of the third.
New York captain Jaromir Jagr, who has only one goal in eight games, had two good scoring chances in each of the first two periods. He just missed scoring on a wraparound and had a redirection attempt go wide in the first. During the second, Smith turned aside two shots from the right circle.
"They had nothing to lose," Jagr said. "Skating up and down, they had more scoring chances than us."
Jagr stole an errant pass by Smith in the slot with six minutes left in the game, but a sliding Picard stopped his shot.
"A big save by Pic," Smith said. "The shutout goes to him, I guess. I said, 'I'd kiss you after the game,' and I did."
Ouellet scored an empty-net goal with 57.2 seconds left, off an assist from Smith.
"I don't know if we deserved a point tonight because it felt like they played better than us from the start," Lundqvist said.
Tampa Bay captain Tim Taylor (hip surgery) was on the ice for the first time this season with his teammates during the morning skate. ... It took the Rangers 14 minutes to record their first shot of the second period. They were outshot 16-4 during the frame. ... Lightning D Mike Lundin injured his left ankle midway through the second and didn't return.
Copyright by STATS LLC and The Associated Press
Arena: Amalie Arena Location: Tampa, Florida
Referees: Chris Rooney, Ian Walsh Linesmen: Andy McElman, Vaughan Rody
Attendance: 20,926 (109.0% full)
Team Stat Comparison
Power Play Goals
Power Play Opportunities
Shots on Goal
No scoring this period
Alexandre Picard (2)
Assists: Jeff Halpern, Mathieu Darche
Martin St. Louis (23)
(Power Play) Assists: Jussi Jokinen, Dan Boyle
Michel Ouellet (15)
(Empty Net) Assist: Mike Smith