Bielsa had won the first two games in the Championship since taking over at Elland Road, and was looking to carry that form in to the cup compeition.
The team was changed significantly from the 4-1 drubbing against Derby County at the weekend, with the likes of Jamal Blackman and Lewis Baker (both on loan from Chelsea) getting a game for against Bolton.
It took 27 minutes for the dealock to be broken, as new £10 million signing Patrick Bamford latched on to a pass from Samuel Saiz to side-foot the ball home well.
The Yorkshire club doubled their lead when Saiz turned goalscorer, as he got cut inside to leave two defenders for dead before finishing under Bolton's Remy Matthews in net.
Bolton managed to get back in to the game shortly in to the second half through Erhun Otzumer hit the ball home past Blackman in goal who was unsighted by a crowd of players, but weren't able to get an equaliser as they dropped out of the competition in the first round.