"They weren't beautiful goals at all, just shots on net going in," Lecavalier said. "They've been tough to get this year."
Alex Tanguay had a goal and two assists and Martin St. Louis also scored for the Lightning, who have recorded points in six straight games -- four wins and two overtime losses.
Adrian Aucoin scored the lone goal for the Coyotes, who have dropped five of their past seven.
Phoenix's already thin defensive corps took an additional hit with 3:35 left in the first period when Jim Vandermeer was whistled for a 5-minute major penalty and a game misconduct for running Kurtis Foster into the right half boards.
"You're certainly disappointed to lose a guy, especially a veteran guy, but you play the hand you're dealt," said Coyotes coach Dave Tippett. "You can't fault our guys with effort. We had a lot of guys try real hard."
Lecavalier gave the Lightning a 1-0 lead at 5:59 of the first period, beating Jason LaBarbera on a soft backhand shot from the right faceoff circle.
Tanguay made it 2-0 with the Lightning on a 5-on-3 power play, scoring on a quick rebound from the right edge of the crease after LaBarbera stopped Ryan Malone's original shot.
"We're always prepared to kill penalties but especially in the last few games it seems like we're taking penalties early in the game," Aucoin said. "We're a group that needs everyone to play well and when you go a man short and only certain guys are getting on the ice, the other guys stiffen up and it's really hard to get a good rotation."
Aucoin pulled the Coyotes within a goal on a blast from the point with 40 seconds left in the opening period, but St. Louis restored the Lightning's two-goal lead when he put home his own rebound at 4:30 of the second.
"Those guys are the backbone of this team," Smith said. "When they're contributing offensively it's tough for this team to lose."
Lecavalier capped the scoring with 8:14 left with a shot that bounced off the inside of LaBarbera's right pad and the goalie's left skate before going into the net.
That was more than enough for Smith, who made his first start since allowing five goals on 18 shots against Philadelphia on Nov. 2.
"His temperament before the game, there was a good coolness and confidence from him," Lightning coach Rick Tocchet said. "We're getting some pretty good goaltending on this hockey club. Good goaltending makes anything look better."
Phoenix center Peter Mueller left the game with 24.2 seconds to go in the second period after sustaining an apparent lower-body injury and did not return.
Lecavalier had only one goal in his previous eight games. ... The Coyotes already were without defensemen Zbynek Michalek, Kurt Sauer and Ed Jovanovski. Sauer and Michalek are on injured reserve and Jovanovski missed his fourth straight game with a lower-body injury. Phoenix center Matthew Lombardi was a game-time scratch with a lower-body injury. ... NHL commissioner Gary Bettman met with officials from the city of Glendale earlier Monday to discuss the state of the league's attempt to sell the Coyotes to an owner committed to keeping the team in the Phoenix area. The NHL purchased the team on November 2 to end the franchise's summer-long saga in bankruptcy court. ... The announced crowd was 9,503, ending a three-game streak of five-figure attendance.