Niskanen also scored early in the second period, Chris Kunitz had a goal late in the third, while Sidney Crosby supplied assists on all three goals for the Penguins, who snapped a season high-tying three-game losing streak. Marc-Andre Fleury stopped 18 shots for the win.
"The way we played was good, and if we lost there would have been nothing to be mad about," said Fleury.
Patric Hornqvist had the lone goal of the game for the Predators, who have dropped five of their last six games.
Nashville welcomed back Pekka Rinne to the net on Tuesday, and he gave 16 saves in the loss. The two-time Vezina finalist had missed 51 games with an infection in his surgically repaired hip.
"It's great to be back because it's been a long time so it meant a lot to me," said Rinne. "Especially being at home in front of the crowd, it felt good tonight."
With the score tied in the third, Pittsburgh went on the power play as David Legwand was called for hooking at 6:47.
Fleury had come way out of his net to poke a loose puck out of harms way, and Crosby skated down the other way. From the right circle he dropped it back to the point for Evgeni Malkin, who sent it over to the left and Niskanen's one- timer found the back of the net at 7:29.
Pittsburgh grabbed an insurance goal with 2:55 to play as Crosby sent a pass from the left wing to the slot where Kunitz one-timed it home for a 3-1 lead.
After a scoreless first period, the Penguins needed just 27 seconds to get on the board in the second when Crosby's pass from behind the net to the right circle was one-timed in by Niskanen.
It took just 12 seconds, though, for the Predators to tie the game when Hornqvist banged in a rebound from in front.
Pittsburgh continues its five-game road trip in San Jose on Thursday ... Nashville hosts St. Louis on Thursday ... Pittsburgh has won four straight against Nashville ... The Pens were 1-for-5 on the power play, while the Preds finished scoreless on four attempts ... Crosby leads the NHL with 83 points and 54 assists on the season.