Rodrigo glanced home a header from Jack Harrison's free kick in the 37th minute and the roles were reversed for the third goal in the 69th, when Rodrigo arrived in the area to meet a cross with a mis-hit shot that was turned in from close range by Harrison.
Koulibaly, one of Chelsea's offseason signings, received his second yellow card in the 84th for pulling back the jersey of substitute Joe Gelhardt.
Chelsea's poor performance contrasted sharply with its impressive display in a 2-2 draw with Tottenham last weekend and highlighted a number of weaknesses in its squad.
Notably in attack, where manager Thomas Tuchel looks to be short after letting go Romelu Lukaku and Timo Werner and only bringing in Raheem Sterling from Manchester City. Sterling had a goal disallowed in the first half and also missed a great early chance.
Chelsea also has a shortage of center backs - the suspension of Koulibaly won't help - as well as issues in midfield, with N'Golo Kante and Mateo Kovacic injured.
Leeds has opened with two wins and a draw in manager Jesse Marsch's first full season in charge.Spain striker Rodrigo has four goals, making him the top scorer in the league.