The win was Winnipeg's fourth straight to start the NHL season.
Connor Hellebuyck made 19 saves for Winnipeg, as they moved to 4-0-0.
Josh Morrissey and Kyle Connor also scored for the Jets.
Vladislav Namestnikov had three assists for Winnipeg.
Gabriel Valardi chipped in a pair of assists for Winnipeg.
Tyler Toffoli had a goal and an assist for San Jose.
Luke Kunin and Fabian Zetterlund also scored for the Sharks.
Mikael Granlund had a pair of assists for San Jose.
Mackenzie Blackwood and Vitek Vanecek combined to make 30 saves for San Jose, who have yet to win this season (0-3-2).
Josh Morrissey put Winnipeg on the board just under two minutes into the opening frame when he took a partner pass from Colin Miller before moving in and beating Mackenzie Blackwood with a low glove side wrister.
The goal was his first of the season.
Nikolaj Ehlers made it 2-0 with a power play goal at 9:25 when Gabriel Vilardi found him alone on the right side of the San Jose net. The Jet winger made no mistake, firing a high wrister past Vanecek.
Tyler Toffoli cut the Jets early lead in half with a power play marker when he tipped a Jake Walman slap shot past Hellebuyck at 11:43. The goal was his fourth of the season.
Ehlers scored his second of the period at 13:31 when Cole Perfetti hit him with a cross ice feed before the Jet winger moved in and fired a wrister past Blackwood beating him high blocker side to make it 3-1 Jets.
The goal was his second of the season.
Neal Pionk scored on the power play through a screen at to make it 4-1 Jets at 18:48.
Kyle Connor fired his third of the season 1:48 into the second period to chase Vanecek from the game, beating him high blocker side to make it 5-1 Winnipeg.
Both teams next see action on Sunday as Winnipeg hosts Pittsburgh and San Jose returns home to host Colorado.
SHOTS-SAN JOSE WINNIPEG
ATTENDANCE-13,422