Goals apiece from Mateusz Klich and Ezgjan Alioski -plus a Kemar Roofe's double - saw Leeds overcome their hosts.
Derby County lost on Saturday.
Following a 3-1 win over Stoke last weekend, Leeds were in good form again as former Argentina and Marseille coach Bielsa won his battle with ex-Chelsea star Lampard, who was taking charge of the Rams at home for the first time.
Lampard has been active in the transfer window, bringing in nine players including Jack Marriott, Martyn Waghorn, Fikayo Tomori, Mason Mount and Harry Wilson. While the defenders stood off him the Polish midfielder calmly picked his spot and curled a shot beyond the reach of Scott Carson for his second goal in two games this season.
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Bernard , a 25-year-old capped 14 times by Brazil, was a free agent after his contract with Shakhtar Donetsk expired. The Colombian centre-back had been linked to Manchester United and Lyon as well as the Toffees this summer.
And while Leeds 'keeper Bailey Peacock-Farrell definitely could have done better, there's no denying the quality of the hit. Tom Lawrence's direct running was too much for Luke Ayling, the right-back bringing down the Welsh worldwide outside the corner of the penalty area. Lawrence smashed the free kick over the wall and through the grasp of Peacock-Farrell, who appeared to have the shot covered but could not stop it.
In the aftermath, many social media users had their say about the Rams' below-par display.
Craig Bryson has urged Derby County to "dust themselves off and stick together" following a 4-1 defeat to Leeds United on Saturday evening at Pride Park Stadium. The 25-year-old striker still had a lot of work to do when he received the ball from Klich in a crowded penalty box.
Parity did not last long, however, with Kemar Roofe restoring the visitors' lead with a commanding header before the forward added his second with a sumptuous turn and finish after the break.