Ty Conklin made 34 saves on 35 shots to earn the win.
Hossa opened the game's scoring on a Detroit power play at 6:51 of the first period. He broke free of a San Jose defender and skated free into the right faceoff circle before snapping a shot that snuck through Evgeni Nabokov's pads and into the net.
Leino's eventual game-winner came with 3:52 left in the opening period as he reached to bat a fluttering puck out of mid-air and into an open net.
Zetterberg scored his first of the game on a highlight-reel play at 4:08 of the middle frame.
With Pavel Datsyuk in the penalty box, Zetterberg blocked a shot in his own end and raced out into the neutral zone where he picked the puck back up. Fighting off a defender, Zetterberg did a spin-o-rama between the faceoff circles and slid the puck around Nabokov.
The superstar Swede added Detroit's final goal with 2:57 left in the game, stuffing the puck between Nabokov's pad and the post from behind the net on a Red Wings five-on-three.
Christian Erhoff scored San Jose's lone goal at 6:25 of the second, beating Conklin with a long shot on a Sharks powerplay.
Notes: Hossa left the game during the second period after taking a hit to the head. The Red Wings said he was kept out for precautionary reasons... Datsyuk's assist on Zetterberg's second goal was his 500th career point... The Sharks had an apparent goal negated by video review in the second period... Just before Zetterberg's first goal, the puck bounced off the protective netting in the Detroit zone but no official noticed.