The Colombian allowed Pumas substitute Pablo Barrera's weak shot across goal to slip through his hands and into the net in the 107th minute.
The goal gave Pumas a 3-2 aggregate win in the Clausura championship final as they clinched their sixth domestic title and their first since 2004.
Pachuca midfielder Cristian Gimenez celebrated his first Argentina call-up by twice putting the home team ahead in a game which also produced an extraordinary Pumas miss.
Pachuca, also attempting to win their sixth title, went ahead in the 21st minute when Gimenez converted a penalty after Blas Perez was pushed by Efrain Juarez.
Paraguay forward Dante Lopez equalised with a shot on the turn in the 62nd minute but Gimenez put the Beavers back in front when he scored with a low free kick 16 minutes later, his 13th goal of the championship.
Pachuca had Javier Munoz sent off in the 90th minute for a lunging tackle on Martin Bravo and the game went to extra-time as the away goals rule is not used.
Pumas missed an extraordinary chance in the first period when Bravo slipped between two defenders and shot against the inside of the post.
The ball rebounded across the face of the goal but Bravo failed to make contact and Lopez shot wide from point-blank range.
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