Miguel Almirón played the full game Santiago de Chile, but after a goalless first half, La Albirroja fell behind when Blackburn Rovers' Ben Brereton opened the scoring before Mauricio Isla added the second.
The result leaves Paraguay sixth in the CONMEBOL table, with four teams automatically qualifying for Qatar. Paraguay face Bolivia - currently in ninth position - in La Paz on Thursday.
After that, Almirón will return to Tyneside, and should find that process more straightforward than initially feared, with 47 countries - including Bolivia - taken off the travel red list on Monday morning.