Hornqvist and Sergei Kostitsyn each had a goal and an assist for the Predators, who weathered Anaheim's 41-24 shot advantage with several big saves by Rinne before scoring two empty-net goals in the final minute.
Jerred Smithson scored the first goal for Nashville, which has won three straight -- all with Rinne in net -- after a five-game skid.
"We played really well defensively, which is great to see at the start of a road trip," Rinne said. "We know it's going to be a really tough road trip out here, but we stuck together defensively. They got a lot of shots, but we didn't give them so many good chances. We just have a strong defensive core. That's our backbone."
Saku Koivu scored with 8:14 to play for the Ducks, whose three-game winning streak ended. Anaheim had won four straight at home since Dec. 5, but couldn't crack Nashville's defense, which has allowed a Western Conference-low 94 goals.
Kostitsyn and Shea Weber both scored into an empty net as the Predators opened a three-game California trip.
Jonas Hiller stopped 20 shots for Anaheim in the third game of a six-game homestand, but the Ducks were punchless on offense just a few hours after learning they'll be without captain Ryan Getzlaf for another 3-5 weeks. The high-scoring center has broken bones in his face after getting hit with a puck Dec. 28.
Bobby Ryan has taken over Getzlaf's spot in the middle of the Ducks' top line with Corey Perry. Anaheim coach Randy Carlyle tried Matt Beleskey and newcomer Maxim Lapierre with his remaining stars, but neither generated any offense.
"We just didn't have it tonight," said Koivu, who scored his 11th goal on a sharp pass from Dan Sexton. "We worked, but we just weren't hungry enough and desperate enough to get into the areas where we could get those loose pucks and rebounds. There were a lot of shots and we created a lot of cycles, but we weren't able to create a lot of quality chances."
Lapierre made his debut with the Ducks, who acquired him in a trade with Montreal last week. The Canadian center wasn't able to play until getting a U.S. work visa, which he didn't need while playing for the Canadiens.
The Predators scored first when Smithson jabbed a loose puck past Hiller during a scramble in the crease 5:10 into the first period, with the goal upheld after a lengthy video review. The goal was just the fourth of the season for the defense-minded forward, ending a nine-game drought.
Nashville went up 2-0 early in the second period when an Anaheim defensive mix-up left Kostitsyn totally unchecked in a faceoff circle. Hornqvist deflected home a pass while easily fending off a defender near the crease.
"That was a tough way to start, especially against a team that plays that solid in their own zone," Hiller said. "It looked like we were expecting good things to happen for us, but we forgot to work for it. We had a lot of shots, but a lot of them were from the outside. It seemed like we weren't desperate to get near the net, and we made bad turnovers."
Anaheim outshot the Predators 28-16 in the first two periods, and Beleskey and Lubomir Visnosky both rang pucks off the post.
"You talk about hockey gods -- they hit two posts, and they hit them early," Nashville coach Barry Trotz said. "If they go in, maybe they change the whole complexion of the game."
Material from wire services and team media was used in this report.
1 - 0 NSH
2 - 0 NSH
2 - 1 NSH