"He had a really good week of practice," Tampa Bay coach Rick Tocchet said. "When he practices well he's right on."
Smith, who missed the final 32 games last season because of post concussion syndrome, made 32 saves to stop a personal six-game losing streak with his first victory since Jan. 27.
"I worked really hard in practice this week and things turned out great for us," Smith said. "I got back to fundamentals this week. I think it helped, so hopefully it can carryover."
Steven Stamkos had two goals and Andrej Meszaros and Ryan Malone also scored for the Lightning, who were outscored 11-2 in losing their previous two games.
San Jose got goals from Ryan Vesce and Dan Boyle. The Sharks are 2-2 during a six-game trip.
"We're just not playing the full 60 minutes," Boyle said. "We're making some mistakes and they're costing us goals."
Wright's first goal -- in the eighth game of his rookie season -- came from the low slot off a pass from Martin St. Louis just 30 seconds into the game. St. Louis has started the season with a point in eight consecutive, picking up nine assists and 12 points over the stretch.
"He's a breath of fresh air," Tocchet said of Wright. "He's a 19-year old that does what you ask."
Malone made it 2-0 when he redirected David Hale's shot for his seventh goal this season with 4:59 left in the first.
"Once again our start isn't the way it should be, so as a coach I'll have some questions to ask some of the leaders," San Jose coach Todd McLellan said. "We'll be looking for some answers."
The Sharks rebounded from a 2-0 deficit to beat the New York Rangers 7-3 on Monday night.
San Jose got to 2-1 on Vesce's goal from in-close at 12:34 of the second. He has a goal in three straight games.
Tampa Bay went ahead 3-1 with 3:21 to go in the second on Stamkos' fifth goal of the season. Meszaros extended Tampa Bay's advantage to three goals early in the third.
Boyle scored a power-play goal with 6:19 remaining in the third.
Stamkos had an empty-netter during the final minute.
Vincent Lecavalier's goal-scoring drought reached 15 consecutive games, dating to March 17. The Lightning captain did get his seventh assist on Wright's goal.
NOTES: San Jose won both games against Tampa Bay last season, outscoring the Lightning 10-1. This was the lone game between the teams this season. ... Stamkos has four goals and six points over the past four games. ... Sharks D Jason Demers assisted on Vesce's goal and has five assists in his last three games. ... Sharks C Joe Thornton tied San Jose GM Doug Wilson and Dave Keon for 74th on the career assists list (590) when he assisted on Boyle's goal.