The Lightning answered with a power-play goal by Gourde at 18:57 on a putback to make it 1-1.
"I think we showed the depth of our team tonight," Gourde said. "Every line can score and every line was effective during this homestand. If we keep going that way, we're going to win more games than we lose."
Sergachev gave the Lightning a 2-1 lead at 16:39 of the second period with a spin-around wrist shot from the high slot.
"I was trying to go down and get the puck from [Tyler Johnson] and I saw no play there, so I turned and turned back and ... lucky goal," Sergachev said. "I probably tried to do that in juniors before, but not here."
Connor made it 2-2 at 18:02 of the second period with a tip-in off a shot by Morrissey.
"I don't think we were as sharp and quick as we're capable of being," Jets coach Paul Maurice said. "But a pretty good fight tonight. I wanted us to get better as the game went on and I thought we did that."