The Red Wings scored twice in the final six minutes of the second period to tie the game. Helm made it 2-1 with 5:07 left when he put in a loose puck from the crease. It was his first goal of the series.
Nyquist tied it with 10 seconds left. He one-timed a shot past Bishop from below the right circle off a pass from Riley Sheahan. It was Nyquist's first goal of the playoffs and fourth goal in 34 Stanley Cup Playoff games.
"I think it got us back on track there for a little bit. It would have been nice to feed off that big second-period finish that we had, going into the third," Helm said. "It would have been nice if we kept that momentum going a little bit harder and thrown a few more pucks at the net and been able to score one. That didn't happen tonight."
Tampa Bay can end the series Thursday. The Lightning needed seven games to eliminate the Red Wings in the first round last year.
"When you have a chance to win a series at home, you want to do it," Cooper said. "It's rest, travel, jumping on a plane, more hotels, that's the part that wears on you."