Early Paleozoic paleomagnetic data from NW Argentina and Northern Chile have shown large systematic rotations within two domains: one composed of the Western Puna that yields very large (up to 80°) counterclockwise rotations, and the other formed by the Famatina Ranges and the Eastern Puna that shows (*40°) clockwise rotations around vertical axes. In several locations, lack of significant rotations in younger rocks constrains this kinematic pattern to have occurred during the Paleozoic. Previous tectonic models have explained these rotations as indicative of rigid-body rotations of large para-autochthonous crustal blocks or terranes. A different but simple tectonic model that accounts for this pattern is presented in which rotations are associated to crustal shortening and tectonic escape due to the collision of the allochthonous terrane of Precordillera in the Late Ordovician. This collision should have generated dextral shear zones in the back arc region of the convergent SW Gondwana margin, where systematic domino-like clockwise rotations of small crustal blocks accommodate crustal shortening. The Western Puna block, bordering the Precordillera terrane to the north, might have rotated counterclockwise as an independent microplate due to tectonic escape processes, in a fashion similar to the present-day relationship between the Anatolia block and the Arabian microplate.