Czech Republic international Vydra scored either side of a missed penalty from Sebastian Larsson, with Johnson netting in each half to consign Hull to a 21st winless away league match in succession.
Derby went ahead at Pride Park when Vydra curled in a powerful 15th-minute free-kick from the edge of the box, but the visitors had a chance to equalise before the half-hour mark.
Tom Lawrence dragged Ola Aina to ground inside the box and referee Darren Bond awarded a spot-kick that Larsson blasted well over the crossbar.
Vydra punished the Swede's miss when he rifled into the net at the end of a slick move and Curtis Davies added to Hull's problems by heading home against his former club four minutes later.
Johnson turned home a right-wing cross from Lawrence on the stroke of half-time and placed a cool, curling finish into the bottom-left corner to add further gloss to an emphatic result.
David Meyler clipped the crossbar in the 88th minute, but a goal would have been scant consolation for Leonid Slutsky's Hull, which slipedp to 10th as Derby moved to fourth.