Cody McLeod, P.K. Subban and Viktor Arvidsson also scored for Nashville, which has won three straight and six of seven. Craig Smith and Colin Wilson had three assists apiece to help the Predators move a point ahead of St. Louis for third place in the Central Division.
Pekka Rinne made 26 saves in winning his fifth consecutive start.
San Jose allowed six goals in Friday night's loss at Dallas.
Sissons scored the game's first goal at 4:14 of the opening period.
Behind the San Jose net, Smith battled with Tomas Hertl and passed the puck off the back of the cage to Wilson on the left side. He made a spinning backhand pass to Sissons just outside the slot, and he beat Sharks goaltender Martin Jones with a backhand to the stick side.
McLeod made it 2-0 at 15:19 of the first.
Roman Josi carried the puck up the left side. Inside the San Jose blue line, he went past Sharks defenseman Brent Burns near the left wall. From the left faceoff dot, Josi's wrist shot deflected off Jones' jersey and then the crossbar before landing on the goal line, where McLeod was there to tap it in for his fifth goal of the season.
Marleau cut the Nashville lead in half at 4:24 of the second with a power-play goal when he deflected Burns' slap shot from the high slot by Rinne for his 26th of the season.
Nashville regained its two-goal lead 24 seconds later when Neal scored on the power play with a wrist shot from the left circle.
Subban's slap shot from the right wall made it 4-1 at 14:39. Braun concluded the second-period scoring at 16:19 when he beat Rinne from the left circle with a wrist shot on the stick side.
Sissons got his second of the game at 5:27 of the third on a deflection of Smith's shot.
Smith has six assists over his last three games. Sissons has three goals in his last two games.
Neal added a power-play goal at 17:01 of the third, and Viktor Arvidsson scored a short-handed goal with 37 seconds remaining.
Jones finished with 27 saves.
San Jose D Marc-Edouard Vlasic missed the game due to an illness. ... Sharks C Joe Pavelski played in his 800th NHL game. ... Nashville C Mike Fisher missed his second consecutive game with a lower-body injury. ... Tennessee Titans Pro Bowl defensive lineman Jurrell Casey attended the game. ... Rinne was honored by the NHL before the opening faceoff for playing his 500th career game on March 16.
Sharks: Host the New York Rangers on Tuesday.
Predators: At the New York Islanders on Monday.