Try hitting it with a broad leaf herbicide like Weed Out from your home and garden store. I think it has mecoprop, dicamba, and either MCPA or 24D. It won't kill it, but it should suppress it enough to let your lawn become more competitive.
Creeping perennials are very tough to control. Usually only a non selective herbicide such as glyphosate (Roundup) will completely control it. Down side is, it kills everything. If it is only along the fence, I would spray it with Roundup in the fall. Then cut out the sod and replace it in the spring or later in the fall.
I'm going to be doing the same thing with some quack grass in my yard.
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