The world number 111 picked up only his fourth tour-level win of the season to see off the number six seed 6-2 6-2 in less than an hour at the ATP 250 clay event in Bastad.
Chardy made it to the fourth round at Wimbledon recently but won less than half of the points on his first serve as he was broken five times by the Uruguayan.
World number 35 Chardy was the highest seed in action on the second day of the competition, with Carlos Berlocq and Pablo Carreno Busta - seeded seventh and eighth - both winning through.
Carreno Busta was comfortable in a 6-3 6-4 win over Dustin Brown, but defending champion Berlocq was required to come from a set down against Julian Reister.
After a poor start, Berlocq held serve throughout the final two sets to set up a clash with Moldova's world number 229 Radu Albot, who upset France's Kenny de Schepper 7-6 (7-4) 6-1.
Fellow Frenchman Paul-Henri Mathieu also went out - as he was forced to retire injured at 5-2 down against Argentina's Renzo Olivo.
Victor Hanescu booked a second-round clash with top seed and two-time champion David Ferrer, sweeping aside Spain's Pablo Andujar 6-4 6-4.
There was better news for Andujar's compatriot Albert Ramos-Vinolas, a quarter-finalist in Bastad last year.
The Spanish qualifier earned a 7-5 6-2 win over Jiri Vesely, who is ranked 22 places higher.
Swedish wildcards Christian Lindell and Elias Ymer each gave the home crowd something to cheer as they won through in straight sets.
Lindell was too strong for Spanish qualifier Inigo Cervantes while Ymer saw off Kazakhstan's Mikhail Kukushkin, the world number 52.