Newlands were the better side in the first half and goals from Stew Bates and Liam Mancrief put them into a commanding 2-0 lead.
That lead was crucially halved right before the half-time whistle, Martin Cooper cutting in from the flank and firing in.
Pier were level on the hour mark, Rich Tolliday timing his run to perfection and stooping to fire an unstoppable header into the back of net from Cooper's cross.
Andy Spivey's side took a 3-2 lead with 15 minutes left on the clock when a high ball was allowed to bounce twice and Gary Thomas out-jumped Newlands keeper Will Rowley and headed Pier into the lead for the first time in the game.
Pier's win was confirmed when Tolliday was fed the ball out wide and he left fly with a rasping drive 35 yards out that flew in to wrap up the scoring.
Boss Spivey singled out Tolliday as his side's man of the match, while Kyle Spivey also impressed.