West Yorkshire outfit Leeds took the lead as early as the third minute from the penalty spot. Andy Lonergan brought down Sam Byram inside the Bolton box, and Rodolph Austin slotted home the spot kick with ease.
Steve Morison came close for Leeds just four minutes later, while Byram saw a header saved on 18 minutes.
Eidur Gudjohnsen, Matt Mills, Liam Trotter and Darren Pratley all had chances for hosts Bolton in the first half, but Leeds went into the half-time interval 1-0 up.
It was 1-1 just three minutes into the second half, though. Luke Murphy brought down Darren Pratley inside the Leeds box, and Gudjohnsen slotted home the resulting spot kick.
Lewis Cook, Murphy, Gaetano Berardi and Casper Sloth all had chances for Leeds, but the visitors had to settle for a point.