Tyson put the Rams ahead for a third time after Conor Sammon's two goals were cancelled out by Marlon King's penalty and a Peter Lovenkrands header.
Blues went into the game looking for a first win in three and it was they who threatened first when Serbian striker Nikola Zigic teed-up Hayden Mullins but the midfielder dragged his fifth-minute drive wide.
Wade Elliott was the next to go close for Lee Clark's men when his left-footed effort rustled the side-netting of Adam Legzdins' goal.
Former Wigan man Sammon then put the Rams in front just after the half-hour mark albeit in controversial circumstances.
Michael Jacobs cut in from the left to fire a right-footed shot which Butland turned onto the left-hand upright only for the for the Irish striker, who was clearly stood in an offside position, to head his third goal of the season into the empty net.
Nigel Clough's men pushed for a second and Theo Robinson saw an effort deflected behind before Craig Bryson fired over when well-placed inside the penalty area following John Brayford's cutback.
Home fans appealed for a penalty a minute before the break after winger Jacobs tussled with Jonathan Spector but referee Nigel Miller opted to book the 21-year-old wideman for diving.
Marlon King came close to restoring parity 11 minutes into the second period but, after breaking clear, he was narrowly beaten to the ball by keeper Legzdins which bounced off the Blues striker and behind for a goal kick.
Sammon's curling effort at the other end three minutes later was easily claimed by Butland before full-back Spector was booked following a rash challenge on Jacobs.
Robinson should have doubled Derby's lead in the 63rd minute, but he powered a left-footed effort over the bar after pulling off Blues defender Curtis Davies.
The Rams' 17-year-old midfielder Will Hughes tested Butland from range after 67 minutes before Blues' West Ham loanee Robert Hall flashed a shot wide and fellow substitute Lovenkrands curled a free-kick over from the edge of the box.
King then levelled proceedings from the penalty spot, sending Legzdins the wrong way following Richard Keogh's foul on teenager Hall.
The Blues striker almost put his side ahead five minutes later when his deflected shot came back off the Derby crossbar.
Sammon scuffed a left-footed shot across Butland and into the far corner to restore the lead 10 minutes from time, only for substitute Lovenkrands to flick Spector's right-wing cross past Legzdins two minutes later.
But the home side were not to be denied and Tyson, who replaced Robinson in the 72nd minute, poked in Jacobs' centre to extend Blues' winless run to three games.