Curtis Rose edged Rovers ahead after 15 minutes, but that provoked a superb reaction from Pier, who were soon level via Martin Cooper's goal following Gaz Thomas' flick-on.
It was soon 2-1 to Pier, debutant Isaac Sands rounding off a slick team move, before veteran defender Steve Sheader rifled in from close-range for 3-1.
Jack Ramos curled in superbly to make it 3-2 and give Rovers hope, but debutant and man of the match Sands scored the goal of the game almost immediately to round things off for Pier, finishing off Jamie Bradshaw's cross after a raking pass from Gaz Thomas.
Sands was Pier's star man, while George and Curtis Rose impressed for promoted Rovers.
Edgehill had to settle for a share of the spoils from their trip to Hunmanby United.
Joe Gallagher opened the scoring for Steve Clegg's side 20 minutes in with what proved to be the only goal of the first half.
Cameron Dobson netted twice after the break to turn the game on its head and hand United the lead, but Kurt Henderson grabbed a share of the spoils for Edgehill, who had Frank Belt sent off.
United stopper Kyle Scaife was man of the match for the hosts, while Ricky Nock shone for Edgehill.
Filey Town were made to work hard for their third successive win of the new campaign, falling 2-0 behind before beating promoted Scalby 4-2.
Youngster Max McNiven handed Scalby the lead with a superb strike, before new signing Kyle O'Toole doubled the Otters' advantage, tapping in after the Town keeper spilled Paul Oldroyd's free-kick.
Debutant striker Ash Robinson halved the deficit for Town, who should've gone in level at the break, but were denied by a stunning last-ditch block by David Oxley on the Scalby line.
Town levelled from the penalty spot, Robinson grabbing his second, before goals from Ryan Tranmer and Lalan Flynn wrapped up a hard-fought 4-2 win.
Robinson was named as Town's star man, while young midfielder Brad Smith stood out for Sam Medd's Scalby.
Seamer produced a slick second-half performance to beat Goal Sports 3-0.
The sides went in level at the break, but two second-half strikes from Danny Glendinning and a Kris Tate goal handed Tommy Adams' side the win.
Ellis Howley was Seamer's star man, while Goal Sports boss Mark Plumpton was impressed with his entire team's efforts.
Newlands continued their impressive start to the new season with a 2-1 win on the road at Sherburn.
A Drew McCoubrey penalty and a Stuart Pickard own goal sealed the points for Nick David's Park, for whom striker Luke Delve was named man of the match.
Rodney Lewin netted a late consolation for Sherburn, who had Alex Sheader and Joey Harris in form.