The Jets will be looking to advance to the Western Conference Final with a win over the Predators Monday night in Winnipeg.
Connor, who was scoreless in the playoffs until this point led the four goal outburst by the Jets as they took control of the contest.
Mark Scheifele and Dustin Byfuglien each had a goal and assist and Blake Wheeler had a pair of assists for the Jets, who will look to close out the series Monday night at home.
Paul Stastny, Dustin Byfuglien and Mathieu Perreault also scored for Winnipeg.
Connor Hellebuyck turned aside 38 shots for the Jets.
Yannick Weber and Ryan Johansen scored for Predators.
Pekka Rinne and Juuse Saros combined to stop 26 shots for Nashville.
SHOTS-WINNIPEG 32 NASHVILLE 40