Jones opened the scoring at 11:19 of the first period, beating Jean-Sebastien Giguere with a slap shot to the glove side.
Perry tied it with 1:44 left in the period, skating across the goalmouth and putting a backhander by Rinne's stick.
"The first goal bounces in off of our defenseman," Anaheim coach Randy Carlyle said. "It hits two or three people and then hits our defenseman in the foot and we're down 1-0. But we came back with a big goal. We played with everything we had. You have to like the effort of our hockey club."
Arnott answered off a rebound 1:08 into the second period, and the Predators made it 3-1 when Erat beat Giguere with a wrist shot at 11:22 of the second.
Perry scored again for Anaheim with 1:06 to go in the second, skating in low from the left side and beating Rinne with a low snap shot.
Fiddler added an empty-net goal with 1:11 left in the third.
The Predators won many battles to control the puck.
"That's how you score now is in the hard areas," coach Barry Trotz said. "Those hard areas are right in front of the goaltender, in the crease and from the back door. The blue paint out there is where we want to be.
"Our top guys have responded by saying they are going to get it done. They are doing it collectively. The guys we expect to put up numbers like Arnott, Erat and J.P. Dumont are doing that."
Giguere played his first full game since Jan. 14. He had played only 15 minutes since then -- in a Jan. 21 game against the New York Islanders.
"It's nice to go one full game and have some positives to build on," said Giguere, who stopped 30 shots. "I felt my energy was good. Hopefully, this is the beginning of a better second half."
The Predators scored more than two goals in a game for only the second time in their last 10 games. ... Perry has nine points (eight goals, one assist) in his last nine games. ... Anaheim failed to score a power-play goal for the second straight game after scoring at least one in nine consecutive games.