Mateusz Klich bent home a stunning strike at the end of a thrilling team move to put the visitors in front inside five minutes at Pride Park.
When Tom Lawrence's free-kick was badly misjudged by 21-year-old goalkeeper Bailey Peacock-Farrell the Rams were swiftly level, but Ezgjan Alioski's perfect left-wing cross was headed in by Kemar Roofe to restore the Leeds lead.
Leeds should have made the points safe in the 56th minute but Scott Carson made a magnificent reaction save to keep out another Roofe header.
There was nothing the former England international could do about Roofe's second goal, though, the striker collecting a Klich pass and brilliantly spinning away from two defenders to thunder in a powerful drive that beat Carson at his near post.
Within four minutes, Alioski crashed home a header from Pablo Hernandez's cross to send Leeds second in the Championship with two wins from two fixtures under Bielsa.