Shriever beat defending champion Mariana Pajon in the women’s event minutes after Whyte had finished second in the men’s event.
Shriever had looked the class of the field in qualifying and delivered in the final.
The 22-year-old led from the first bend, holding off a late charge from defending champion Mariana Pajon of Colombia down the final straight.
Whyte had earned Britain’s first BMX racing Olympic medal moments earlier.
The 21-year-old Londoner, having been hampered by poor starts in qualifying, made it into the first corner of the final in second place and held his position as Niek Kimmann took gold for Holland.
The two crossed the line with a healthy margin after a late crash for Frenchman Romain Mahieu split the field, with Colombian Carlos Ramirez Yepes taking bronze.
Whyte had shown in qualifying he had the speed to contend if only he could get off the line, needing to recover from poor starts in the first two runs but then winning the final one to be sure of his place in the final.
And there were no mistakes when it really mattered as Whyte quickly got himself into position.
Defending champion Connor Field of the アメリカ was unable to contest the final after crashing heavily in the last run of his semi-final, leaving the track on a stretcher.