Under a clear blue sky in the alpine resort of Livigno, Italy's Michela Moioli and Lorenzo Sommariva claimed silver, while France's Lea Casta and Loan Bozzolo earned bronze.
Bankes had finished 13th in the women's snowboard cross final on Friday, while Nightingale ended in 26th place in the men's event the previous day.
The winning pair were all smiles on Sunday, however, pumping their fists in the air after climbing onto the top of the podium before closing their eyes to sing the national anthem.
The British, Italian and French medallists capped their victories with group hugs and posed for selfies as France's Bozzolo took out his mobile phone.
Britain were in second place after the first leg of the final run by the men, but Bankes secured them the gold in the second run after she overtook France's Casta.
Home crowd favourite Moioli - part of the Italian mixed team that took silver at the last Olympics - also managed to outrun Casta for the runners-up position.
It was the second Milano Cortina medal for Moioli, who won bronze in the individual women's snowboard cross final last week.
There was disappointment for the USA, the mixed team gold medallists in 2022, as Nick Baumgartner and Faye Thelen, both on their fifth Olympics, were eliminated in the quarter finals.
Australia's Josie Baff, gold medallist in the women's final, missed out on the podium after her partner, Adam Lambert, fell in the first leg of the mixed team final. The pair finished fourth.
