Kris Letang and Conor Sheary also scored for Pittsburgh, which converted three of six power-play chances.
The Capitals (2-1-1) were 0-for-4 with the man advantage. The Penguins (2-1-1) have killed off 17 straight power plays.
Hornqvist missed the first three games of the season following a procedure on his right hand in the offseason. His last goal was the game-winner in Game 6 of the Stanley Cup finals. He also tallied in Pittsburgh's 2-0 Game 7 win in the Eastern Conference semifinals against Washington.
The Capitals' Christian Djoos, making his NHL debut, scored a goal and an assisted on Alex Ovechkin's eighth goal of the season.
With Washington trailing 3-1 in the third, Djoos avoided a Pittsburgh player and slid a pass into the slot that Ovechkin redirected past Murray with 7:09 left to play.
Braden Holtby made 33 saves for Washington.
Pittsburgh took a 1-0 lead at 5:22 of the first. With Matt Niskanen off for slashing, the Capitals came within five seconds of killing off the power play, but during a scramble in front, Bryan Rust pushed the puck across the top of the crease to Letang, who lifted a backhander past Holtby.
The Penguins doubled their lead on a similar scenario at 8:20 of the second. This time, with six seconds left on a penalty to Djoos, Hornqvist poked a loose puck home from just beyond the crease.
Djoos got Washington within 2-1 with 53 seconds left in the middle period when he beat Murray with a one-timer from the right circle off a pass from Lars Eller.
Pittsburgh regained the two-goal margin just 38 seconds into the third period when Sheary, parked to the left of Holtby, redirected a cross-ice pass from Justin Schultz.
NOTES: Penguins RW Patric Hornqvist has eight points (five goals, three assists) in his past 11 regular-season contests against the Capitals. ... Pittsburgh D Ian Cole, who was hit in the face by a slap shot Saturday night, was out of the lineup for the first time since joining the Penguins in March 2015. ... Capitals G Braden Holtby, who won his first two starts of the season, missed winning each of his first three for the first time in his NHL career.