Brian Rolston added the other tally for the Devils, who have won two in a row and four of six overall.
Scott Clemmensen stopped 28 shots for the win.
Brad Boyes and David Backes lit the lamp for the Blues, losers in four of five contests.
Manny Legace allowed four goals on 26 shots for the loss.
The Devils iced the game with a pair of goals late in regulation a little more than two minutes apart.
Parise's second of the contest, resulting from his poke through a goal-mouth scramble, put New Jersey up 3-2 at 14:19. Pandolfo provided some breathing room at 16:33, managing to get his stick on Michael Rupp's shot to deflect it home.
Legace went to the bench with just under a minute to play and Alex Steen made it a one-goal contest with 30 seconds remaining but the Blues could not net the equalizer.
Parise put the Devils on the board just 62 seconds into the contest, and Boyes countered on a rebound goal at 4:19.
Backes finished off a 2-on-1 with a wrister to the near post for a 2-1 St. Louis lead at 7:41 of the first and Legace made the edge stand up by foiling Brian Gionta on a short-handed breakaway late in the period.
Rolston slipped one past Legace's outstretched pad for a 2-2 game 2:37 into the second and the score held until New Jersey's final burst.