Visnovsky took the puck at the blue line after Anaheim won a faceoff in the Sharks' zone and rapped a modest slap shot through traffic into the net at 4:27 of the extra period.
The victory was the fourth in a row for Anaheim and knocked the Sharks down to 1-2-1 in their last four games.
Corey Perry and Jason Blake scored in regulation for the Ducks. Jonas Hiller made 39 saves in goal.
Antero Niittymaki allowed three goals on 20 shots for San Jose. Devin Setoguchi and Torrey Mitchell scored the Sharks' two goals.
Setoguchi's goal at 9:05 of the third period sent the game into overtime. Mitchell's slap shot at 1:42 of the first period gave San Jose an early 1-0 lead.
Anaheim tied it at 9:42 of the first period on Blake's tip-in goal and then took a 2-1 lead at 8:27 of the second period on Perry's backhander of a rebound off a sprawling save by Niittymaki.
Notable deaths of 2014 [PHOTOS]