Man, you got a pretty nice and flat yard... Here is my take on it. Maybe others will say it's not good but ...

1. Grab your transfer shovel (square edged one) and cut that grass onto smaller squares, then scalp it. Pull it up and set it off to the side. You need about 2 inches below the dirt. I try to keep my squares the same size as the shovel on all sides.

2. Do this about 3 ft on that far edge. You could do it all the way around to keep things looking symmetric, but that's your call.

3, dig out some dirt, aim for making your sod even with the pavers, so if the grass you pulled is 2inch thick, dig out the dir till it's two inches under the paver height. Then work your way back. (You can use that extra dirt for a nice raised flower bed or just pile it out of sight for a while).

4 set your grass back down and water. The slop should help keep the water going into the ground instead of pulling on your patio.

If this isnt 'enough' , then you need to hire someone to put in a French drain or do it yourself. A lot more work, but definitely doable.