PDF export of polygons: How to get rid of polygon boundary lines?

For me, AbsoluteThickness[-1] does the trick in

Graphics[{EdgeForm[{White, AbsoluteThickness[-1]}], polygon}, AspectRatio -> 1]

In the final PDF there are slight white lines visible. Those are artifacts of the displaying process (alpha blending) and won't be visible in the final print. Note that the white lines have constant thickness no matter how deep you zoom in.

Update

I downloaded the PDF you provided in the comments and on my OSX here it looks like this

The issue is related to the opacity of the VertexColors. You can easily avoid it in this case by blending into white and not opaque.

data = Table[{x, (x - 5)^2 + 3}, {x, 0, 10}];
p1 = ListLinePlot[data, Filling -> {1 -> {15, {Blue, None}}}]
p1 = Normal@p1 /. 
   Polygon[x_] :> 
    Polygon[x, 
     VertexColors -> (Blend[{RGBColor[0, 0, 1], 
           RGBColor[1, 1, 1]}, #] & /@ Rescale[x[[All, 2]]])];
polygon = First[Cases[Normal@p1, _Polygon, Infinity]];
plt = Graphics[{EdgeForm[None], polygon}, AspectRatio -> 1]

(No hidden lines)

In case you inist having opacity, there are various methods suggested to work around the bug:

• Problem with transparency when I export an eps file
• How can I include graphics with transparency in LaTeX?