The analysis of γ-ray flux variability along with the parsec-scale jet kinematics suggests that the high-energy radiation in the BL Lac object S5 0716+714 has a significant correlation with the mm-VLBI core flux density and with the local orientation of the inner jet flow. For the first time in any blazar, we report a significant correlation between the γ-ray flux variations and the variations in the local orientation of the jet outflow (position angle). We find that the γ-ray flux variations lead the 7 mm VLBI core flux variations by 82±32 days, which suggests that the high-energy emission in S5 0716+714 is coming from a region located 3.8±1.9 parsecs closer to the central black hole than the "core" seen on the mm-VLBI images. The results imply a strong physical and casual connection between γ-ray emission and the inner jet morphology in the source.