I was facing a similar situation and solved it by moving the gutter outlet to the opposite side and changing the slope of the gutter to flow in the same direction. Fortunately, in my case there was another gutter outlet around the corner which I was able to tap into.
Another problem area I am currently facing is a corner of the garage against a bank that was dug into a slope to make room where the gutter installers decided to place the downspout in the corner and let it drain onto the foundation. I plan to solve it in much the same manner except that I will be digging a 3 foot deep trench across the driveway and installing 4 inch PVC to carry the water away. I have to dig the trench so deep because the driveway is beveled against the slope to prevent erosion.
Just remember that water always flows downhill and that solving it sometimes has to be done above grade or by digging a little deeper.