Pekka Rinne made several key saves down the stretch for the Predators, who overcame a two-goal deficit in the third period.
Legwand gave the Predators a 1-0 lead just over a minute into the second period when he slapped in a rebound of a shot by Hornqvist. The puck glanced off Sharks defender Torey Mitchell and into the net.
The Sharks scored the next three goals. Pavelski started the spurt by turning a nice backhanded pass from Couture into a goal just under five minutes into the period.
Havlat's power-play goal was the result of persistence. Couture and Ryane Clowe both had shots that bounced off Rinne's pads, and Havlat poked at the puck twice before wristing a shot into the top left corner.
Couture gave the Sharks a 3-1 advantage in the first minute of the third period.
Hornqvist got the Predators within 3-2 when he knocked in a loose puck from the crease. Suter tied it with a power-play goal a few minutes later.
NOTES: San Jose C Joe Thornton had two assists, giving him 703 and tying him with Jeremy Roenick for 49th place on the career list. ... Legwand has points in four straight games. ... Pavelski has scored a goal in six of his last eight games. ... Hornqvist has a career-best, five-game scoring streak. ... The Sharks outshot Nashville 19-7 in the scoreless first period.