Wilson netted the winning goal with 2:32 left.
"It was really a fast-paced game," Wilson said. "I think to get those two quick goals was great for our team and great for our confidence.
"Winning always feels good. But I think winning in dramatic fashion feels even better."
Wilson skated in on the right side and put in a pass from Steve Sullivan off a 3-on-1 rush.
"Whether it is in practice or in games, Sullivan likes to make the pass," Wilson said. "I was ready for it. He made a great pass and I just let a quick one-timer go."
San Jose coach Todd McLellan admitted his team didn't see the rally coming. The third goal was the one that made him the angriest.
"Nashville is a good hockey team and they are going to push," McLellan said. "I thought we made a few soft plays in the neutral zone that allowed them to come into our zone in the third period.
"Even after it goes 2-2 we should have enough poise and enough composure to manage the game properly to get it to overtime and see what happens there. Our game management was poor at the end. It's unacceptable."
Nashville coach Barry Trotz was also preparing for overtime when Kostitsyn scored.
"I don't know if you think about getting the next goal," Trotz said. "We just wanted to be really strong. There wasn't a whole lot of time on the clock. So you just want to come back after that goal with some good momentum."
The Sharks, who entered the game with the NHL's fourth-most effective power play, had one last chance to gain momentum. With 1:52 left, the Sharks went on the power play when Nashville's Jordin Tootoo shot the puck over the glass for a delay of game penalty.
"There are momentum shifts to a game," Tootoo said. "When we tied up the game with a big goal we got the momentum back and then we got the third one. At that point I have to bear down in our defensive zone and not take penalties like this."
Nashville's Anders Lindback, winner of his fourth consecutive game, withstood the final assault by the Sharks.
"Anders faced some of the best shooters in the world and one of the best lines in the league in Joe Thornton, Patrick Marleau and Dany Heatley," Trotz said. "Anders withstood the pressure very well. That should really help his confidence."
Tootoo had a goal for the Predators, who have at least one point in nine consecutive games.
Niclas Wallin and Dany Heatley scored for the Sharks, who led 1-0 and 2-1.
The Sharks went ahead the first time when Wallin scored with a slap shot from above the left circle at 7:25 of the first period. That quickly ended Lindback's bid for a third straight shutout.
Nashville tied it 12:14 into the second period. Tootoo, battling on the boards behind the net, managed to backhand the puck in front where it was knocked in by San Jose's Scott Nichol, who was stationed at the left post.
"I didn't see what happened," Tootoo said. "I knew a couple of guys were driving hard to the net. I just tried to put it in that area. I didn't know it went in until my teammates started cheering. I was fortunate enough to get a lucky bounce."
The Sharks took a 2-1 lead with 2:34 left in the second. Heatley skated in from the right side and put the puck between Lindback and the right post during a power play.
NOTES: Nashville's Patric Hornqvist was a late scratch with an undisclosed upper body injury. He scored twice in the Predators' previous game Monday against the New York Islanders. ... San Jose beat Nashville three times in four meetings last season. ... -of-four games last season. Nashville RW Wade Belak played for the first time since Nov. 7. ... Kostitsyn has a seven-game point streak.
|Niclas Wallin (3) ASST: Benn Ferriero (3), Justin Braun (7)|
1 - 0 SJS
|Jordin Tootoo (4) ASST: NONE|
1 - 1 Tie
|PPG - Dany Heatley (14) ASST: Joe Thornton (21)|
2 - 1 SJS
|Sergei Kostitsyn (5) ASST: Shea Weber (8), Ryan Suter (9)|
2 - 2 Tie
|Colin Wilson (7) ASST: Steve Sullivan (10), Marcel Goc (8)|
3 - 2 NSH
|Power Play %||21.6%||16.2%|
|% on Road||19.5%||17.2%|
|% at Home||23.8%||15.2%|
|Scott Nichol Hooking against Cal O'Reilly|
|Sergei Kostitsyn Hi-sticking against Derek Joslin|
|Dany Heatley Cross checking against Kevin Klein|
|Dany Heatley Unsportsmanlike conduct|
|Jerred Smithson Hooking against Joe Pavelski|
|Shane O'Brien Tripping against Benn Ferriero|
|Jason Demers Tripping against Marcel Goc|
|Jordin Tootoo Delaying Game-Puck over glass|