Goals apiece from Mateusz Klich and Ezgjan Alioski -plus a Kemar Roofe's double - saw Leeds overcome their hosts.
Alongside Aston Villa and Swansea City, Leeds are one of three sides with a 100 percent start and trail only table-topping Middlesbrough - who have played one more game - after they beat Birmingham City 1-0.
The first chance of the match fell his way as Harry Wilson drove into the penalty area and picked out Waghorn, who could only scuff his shot into the path of Mason Mount. Carson was called into action to deny Roofe at point-blank range with Tomori making a last-ditch block to deny Ayling on the rebound.
Derby's sole comfort was a stellar strike from Tom Lawrence early in the first half.
Roofe slammed the ball high past Carson to register his second of the game.More news: Bitcoin value recovers 3% following delay in pivotal SEC ruling
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But there was nothing that Carson could do about a superb second goal for Roofe on the hour mark as the striker produced a sensational touch to turn Fikayo Tomori to work space for a deadly finish that was smashed into the net.
And within four minutes Alioski crashed home a header from Pablo Hernandez's cross to send Leeds second in the Championship with two wins from their two fixtures under Bielsa.
A 4-1 lead should have then become 5-1 but Saiz sliced an effort wide after a Cooper through ball.
The damage, though, had already been as Leeds cruised to a victory that was even more impressive than the opening weekend win against deposed title favourites Stoke.
The Whites face a test this Saturday away at Derby and Lampard can not help but admit to having been impressed with what he saw at Elland Road, with bags of energy on display from the hosts. Subs not used: Blackman, Jansson, Roberts, Harrison.