Jurrjens (13-5) collected his first victory since July 6, breaking a personal five-game winless streak. He worked out of several jams while allowing eight hits and five walks as the Cubs left 15 men on base.
Freeman gave the Braves a 1-0 lead in the second and Uggla added a blast in the sixth for the National League wild card-leading Braves, who took the opener of a four-game series.
Chicago drew two straight walks from Jonny Venters to lead off the ninth but Venters rebounded by fanning Carlos Pena and Marlon Byrd.
The reliever then stretched his scoreless streak to 24 games when Alfonso Soriano hit a grounder fielded by a sliding Alex Gonzalez, who managed to tag second base for the final out.
Ryan Dempster (10-9) absorbed the loss for Chicago, yielding three runs on six over six innings.
Celebrity Families of 2014 [PHOTOS]