Bishop made his only save of overtime on a breakaway attempt by Hischier at 1:18.
"It's little details that sometimes cost us a goal or a save," Hischier said. "If I score on the breakaway, we win the game. That's a little thing too."
Pavelski scored off a rebound on his backhand in the slot to extend his point streak against the Devils to eight games (six goals, three assists) and goal streak to six games (six goals).
"Sometimes things line up like that," Pavelski said of his success against New Jersey. "But you keep showing up, play hard, work for those chances. When you're hot against a team, you can expect chances and looks.
"On my goal, [Mattias Janmark] makes a good play with his speed and created a chance and I found a loose puck on the rebound."
It was the first goal in nine games for Pavelski.
"It's been different guys at different times; it was great to see him score that one," Stars forward Tyler Seguin said.
Hischier scored off a snap shot from the top of the right circle at 11:53 of the third period to tie it at 2-2.
"We're playing well enough to win a game, but it's just that little step that's missing right now," Hischier said. "It's frustrating but we've got to keep going. We're playing some good hockey."
Kiviranta scored off his own rebound on a snap shot just inside the left post at 5:04 of the third period to give the Stars a 2-1 lead.
"It was great [to see Kiviranta score]," Seguin said. "We've all had our first goal and had that feeling; the confidence he's going to get from it. He's already had a lot of confidence. He's a quiet kid but plays with some swag and it's great for our team for him to start producing."
