Sharp and Kane had goals in the tiebreaker, helping the Blackhawks snap an eight-game losing streak. Robert Lang also scored for the Blackhawks.
"Those two guys, Sharp and Lang, are hot when they play us," Predators coach Barry Trotz said. "They have scored around 65 percent of the goals for Chicago against us this season.
"We try to shut down some of their guys. A lot of their offense comes from Lang and Martin Havlat. We did a fairly good job of shutting them down, but they got their goals."
Sharp was the anchor for the Blackhawks in the shootout, a role he wanted to play.
"I really wanted to shoot," Sharp said. "I was just going to snap it as hard as I could with the fresh ice. I saw that their goalie was really far out so I just put it around him and chipped it into the open net."
It was the second game in a row that the Predators had lost in a shootout.
"Shootouts are what they are," Trotz said. "Shootouts are a one-on-one skills competition. When you win them they are great. When you lose them they are not so great. We have to find ways to win some of those."
Neither team scored in the first period when the Predators held a 16-9 edge in shots.
A little over a minute into the second, Sharp scored the first goal. He skated in from the left side and beat goalie Dan Ellis from close range high to his stick side.
Sharp had one goal in his previous six games, but scored his fourth of the season against the Predators.
Zidlicky tied it 1-1 at 4:49 of the third period on the power play. J.P. Dumont passed him the puck from the right side of the net to the left. Zidlicky fired a one-timer from low inside the left circle behind goalie Patrick Lalime to his stick side.
Lalime saved 35-of-37 shots, winning for the third straight time against the Predators this season.
"Lalime has played two strong games," said Savard. "He will probably get another start. He kept us in there the whole game."
Lang gave the Blackhawks a 2-1 lead at 11:17 with a shot from the left circle that went between Ellis' pads.
Legwand scored on the power play at 14:32 from in front of the crease as he shot the puck between the pads of Lalime.
The Blackhawks failed to take advantage of a power play in overtime.
"It wasn't our best game, but we battled," said Chicago coach Denis Savard. "Nashville came pretty hard at us they played well. The bottom line is we got the win."
- Trotz coached his 700th game with the Predators.
- Nashville forward Darcy Hordichuk left the game with a lower leg injury in the first period and didn't return.
- D Ryan Suter was back on the ice for the Predators after missing the past two games as a healthy scratch.