Backup Carter Hutton made 35 saves in his first career shutout and Roman Josi also scored as the Predators kept their slim playoff hopes alive by beating winning road games on back-to-back nights against Anaheim and San Jose - the top two teams in the Pacific Division.
Nashville is six points behind Dallas for the final playoff spot in the Western Conference with four games remaining.
The Predators' win in Anaheim on Friday kept the Sharks just a point behind the Ducks in the standings but San Jose couldn't capitalize a night later and is running out of time to catch the Ducks after falling flat again against a team likely to miss the postseason.
The Sharks have only three games remaining, including their next contest in Anaheim on Wednesday, but the Ducks still have five games remaining and the inside track on the division title. San Jose is assured of at least second place.
If the Sharks do end up falling short in the division it will be their play at home against some of the league's also-rans that will be a big reason. San Jose has lost five home games since the Olympic break, all to teams that are currently out of playoff position.
The Predators took control of the game in a dominant second period, killing off a pair of penalties and beating Antti Niemi three times.
Hornqvist struck early in the period when he whacked at a rebound of Matt Cullen's shot and knocked it in to extend his goal-scoring streak to four games.
He added his eighth goal in the past 11 games midway through the period just after Nick Spaling came out of the penalty box. Spaling got the puck behind San Jose's net and set up Hornqvist for a one-timer from the slot for his 20th goal of the season.
Hornqvist then got an assist a few minutes later when Josi beat Jason Demers as he drove to the net and chipped a puck over Niemi to make it 3-0.
The Predators have put together an impressive late-season run with points in seven of their past eight games. But it likely won't be enough to overcome a 1-4 homestand after the Olympic break that put Nashville in a deep hole.
NOTES: Nashville swept the three-game season series and has won nine of 14 against the Sharks. ... The Sharks last overcame a 3-0 deficit in the regular season on Feb. 1, 2011, when they rallied for a 5-3 win over Phoenix. ... D Matt Irwin returned to the Sharks lineup in place of Scott Hannan after being a healthy scratch Thursday