Lehtonen made 27 saves for Dallas (38-25-6), which is 5-6-2 in its past 13 games. It holds the first wild card into the Stanley Cup Playoffs from the Western Conference, two points ahead of the Colorado Avalanche.
"It's always a little disappointing to not get points at this time of year," Lehtonen said. "We played careless there, I felt like, through two periods. Too many penalties. [Pittsburgh] is a pretty good team. … We were hanging in there and hoping for a comeback, but that didn't happen tonight."
Hornqvist opened the scoring with his 20th goal of the season. With Marc Methot in the penalty box for cross-checking, Evgeni Malkin passed across the right face-off circle to Hornqvist, who one-timed a shot from the inner edge past Lehtonen's blocker.
Radulov made it 2-1 when he scored on a 5-on-3 at 12:03 of the second period. Spezza passed through the crease to Radulov, who sent a sharp-angle shot past a diving DeSmith.
Hornqvist thought he scored again at 17:28 of the second, but it was overturned following a challenge from the Stars, and it was determined the play was offside.
Malkin scored into an empty net with 43.7 seconds remaining in the third period to make it 3-1. It was his 39th goal of the season, one behind Capitals forward Alex Ovechkin and Winnipeg Jets forward Patrik Laine for the NHL lead.
It was the first of a six-game road trip for the Stars.
"Go back to work and get ready for the next one," Radulov said. "Watch the video. Do some adjustments. We have a long road trip, so we need those points. Today, we didn't play our best, so we have to regroup, adjust and get ready for the next one."