Despite his mistake at the back, Shelvey was involved in most moves for Swansea throughout the first half, but was denied a goal before the break when his long-range free kick drifted over the crossbar.
Swansea manager Garry Monk elected to make 10 changes to his side at the interval, with Alex Sheehan remaining from the team which started the match.
Guadalajara were still a threat going forward after falling behind, but Gerhard Tremmel was a source of frustration for the Mexican side when he tipped Omar Esparza's header wide.
Chances were rare in the closing stages, but there was drama when Taylor and Jesus Sanchez were both shown red cards for clashing off the ball.
A penalty was awarded to Chivas in stoppage time, much to the shock of the Welsh club, due to an apparent collision between a number of players in the box, and Giovani Hernandez stepped up to secure a draw with one of the final kicks of the match.