The shutout was the first for the Ducks since Jan. 17 when Hiller won at Minnesota. He made his fourth consecutive start since Jean-Sebastien Giguere re-aggravated a groin injury.
"We played pretty solid defensively," Hiller said. "I gave up a couple of rebounds, but our defensemen were doing a great job clearing the puck. It's definitely the way we have to play. After we got the first goal, we were able to get that second one and were able to build on that."
Selanne increased his career point total to 1,221, breaking a tie with Beliveau for 38th place. Selanne has played in 1,146 regular-season games, 21 more than Beliveau.
"He's a legend in Montreal, and it's a great honor to pass guys like him because you know you have done some good things in this league," Selanne said. "Things like this are just a bonus for myself. Obviously, I'm very lucky and thankful for how my career has gone."
Todd Marchant scored for Anaheim, snapping his 13-game point drought from the start of the season. Bobby Ryan also had a goal for the Ducks, who had won only one of their previous seven. Saku Koivu and Ryan Getzlaf each had two assists.
"I really hope tonight's game is going to give us the confidence boost that we need," Selanne said. "I'm not very happy about how we played, and this team can play way better than we did. For some reason we were a little too flat, and if seemed to me that there wasn't enough intensity there. But we found a way to win."
Nashville was blanked for the fourth time this season after winning three in a row.
"We tried to generate as many chances as we could, especially on special teams, but we didn't really bear down and put a few home," Predators forward Joel Ward said.
The Predators, who began this four-game road trip averaging the second-fewest penalty minutes in the NHL (9.2), gave Anaheim a two-man advantage for 22 seconds after penalties to Jordin Tootoo and Kevin Klein.
The Ducks capitalized 4 seconds after the first penalty expired, as Selanne got a pass in the slot from Getzlaf and beat Pekka Rinne at 15:32 of the first period. Rinne finished with 27 saves.
Anaheim then scored twice off turnovers in the Nashville zone during the third period with the teams skating 4-on-4. Koivu set up Selanne's eighth of the season and second of the game, and Marchant made it 3-0 when Petteri Nokelainen found him alone in the low shot.
"I didn't expect it to take that long," Marchant said. "Sometimes you just can't figure out how or why or what's going on. But the biggest thing I try to do is just stay positive and keep plugging away and continue to put pucks on the net and do the things that make me successful."
Defenseman Shea Weber, right wing J.P. Dumont and rookie center Colin Wilson, who all played in the Predators' previous game, sat out because of injuries. Weber bruised a foot while blocking a shot, Dumont was hurt during Tuesday's practice, and Wilson had a sore groin.
Martin Erat missed his third game because of a lower body injury, but captain Jason Arnott returned to the Nashville lineup after sitting out six games due to arm and shoulder injuries. Tootoo made his season debut after missing 13 games because of a hip flexor injury and was the 30th player the Predators have used this season, equaling last season's total.
Arnott replaced Weber as the point defenseman on the Predators' power play, which was 0 for 5.
"It wasn't as sharp, no question," coach Barry Trotz said. "We couldn't capitalize on our power play chances. I didn't think we got enough traffic in front on the early power plays. Later on, we tried to do that a little more, but they did a good job defending it."
Anaheim defenseman James Wisniewski completed his two-game suspension for delivering a blow to the forehead of Phoenix's Shane Doan last Saturday.
A moment of silence was held for the victims of Thursday's shooting at an Army base in Fort Hood, Texas. ... Selanne's 587 goals are the most among active players and 18th best overall. ... The Ducks are 17-1-3 against the Predators in Anaheim. Their only regulation loss was Jan. 31, 2001. ... Hiller's only other game against the Predators was Dec. 8, 2007, in a 4-2 loss.
Copyright by STATS LLC and The Associated Press
Arena: Honda Center Location: Anaheim, California
Referees: Tom Kowal, Stephane Auger Linesmen: Jean Morin, Vaughan Rody
Attendance: 14,298 (83.3% full)
Team Stat Comparison
Power Play Goals
Power Play Opportunities
Shots on Goal
Teemu Selanne (7)
(Power Play) Assists: Ryan Getzlaf, Saku Koivu