Buxton's bundled effort came just seconds after the Rams were denied a penalty when Michael Jacobs was brought down in the box.
Prior to that Paul Coutts had netted the rebound from a missed Conor Sammon spot kick, which came just six minutes after substitute Ross McCormack's 67th-minute opener for United.
As a result of the win Derby remain comfortable in mid-table and, although Leeds are one of the other sides in and around them, they are starting to slide.
Sammon received no backing as he appealed for an early penalty - he looked to have slipped as Jason Pearce approached - and that was the only noteworthy incident until the first shot came in the 33rd minute.
Minutes later Leeds' teenage debutant Chris Dawson helped tee up former Derby man Paul Green who cracked the bar from the edge of the box, while at the other end Paddy Kenny was quick off his line to close down Sammon after he beat Pearce to a neat through-ball from Chris Martin.
The momentum did not quite carry over into the second half, though, and it took until the 55th minute for another shot, with Kenny at his best to keep out Davies from the edge of the box and Lee Peltier mopping up the rebound as Martin closed in.
Derby, improving more than their hosts, thought they had taken the lead with 63 minutes gone, as Peltier put a Martin cross through his own goal, but Sammon, no more than an inch ahead of him, was called offside.
Stephen Warnock's corner from the right was not cleared and fell to sub McCormack, who, from his position just outside the area, cracked a first-time curler beyond Fielding and into the top corner.
Leeds' advantage would last just six minutes, though, as Derby got themselves deservedly back on level terms. Not for the first time Pearce was found short of pace and he bundled Martin to the floor, leaving Roger East with a simple decision to make.
Sammon took the responsibility of taking the penalty but proceeded to roll it onto the post, although fortunately for him Coutts was on hand to quickly adjust his body and whip in the second ball.
A second penalty should have followed as White brought down Jacobs six yards inside the area - East awarding a free-kick - but, after Davies' effort was saved by Kenny, the winger's subsequent corner was nodded in by Buxton.