Kevin Klein and Chris Mueller also scored for Nashville, which its third straight.
Martin Erat added two assists for the Predators. He has seven points (one goal, six assists) in his past three games.
Taylor Hall and Shawn Horcoff scored for the Oilers in their third consecutive loss.
Hall opened the scoring at 7:53 of the opening period. The goal was Hall's seventh of the season.
With the Oilers on the power play, Potter's slap shot from the blue line through traffic beat Nashville goaltender Pekka Rinne on the stick side.
The goal was Potter's first of the season.
Kostitsyn answered for Nashville at 11:51 of the first when he converted off a nifty Mike Fisher pass from the right side.
Fisher's assist extended his season-long points streak to seven games.
Klein gave Nashville a 2-1 lead at 4:31 of the second.
From the right circle, Erat found Kostitsyn on the left side. Kostitsyn carried the puck in deep and then fed Klein in the low slot where he had an easy wrist shot into an open net for his second of the season.
In Nashville's March 17 game in Edmonton, it was a bad line change by Kostitsyn that led to an Oilers short-handed goal in a game that Edmonton went on to win 3-2. Kostitsyn was a healthy scratch for Nashville's next game two nights later.
Edmonton got within one at 7:03 of the third when Ales Hemsky's shot from the right side hit Horcoff's skate and squeezed between Rinne's pads.
The Predators are 3-13-1 this season when their opponent scores first, but two of those wins have come in their past three games.
Notes: Edmonton C Ryan Nugent-Hopkins returned the lineup after missing two games with a virus. ... The Oilers have scored a power-play goal in three of their past four games. ... Rinne started his 22nd consecutive game for Nashville. ... Predators RW Patric Hornqvist returned after missing eight games with an upper-body injury.