Thamsanqa Gabuza, who was called up to the Bafana Bafana squad on Thursday for an AFCON qualifier with Nigeria, nodded Pirates ahead in the 19th minute off a corner from Mpho Makola.
Arrows pressed for a way back in the first stanza but Lerato Lamola and Kudakwashe Mahachi could find no way past goalkeeper Jackson Mabokgwane.
However, Lamola equalised on the hour mark following a mistake from Mabokgwane before Zimbabwean hitman Knox Mutizwa scored the winner in stoppage time with a chip.
The result sees Pirates finish 11th on the table with 33 points from 30 matches - five points shy of eighth-placed Abafana Bes'thende.
The Sea Robbers can still salvage a disappointing campaign in their 80th anniversary year when they battle SuperSport United in the Nedbank Cup final at the same venue on June 24.