Vinca Plants

Today:
Running: Nil

Didn't venture past the front gate today, instead tried to tidy up the back yard.
In our yard we have had an unknown vine type plant that has very nicely covered over the back fence. Drought & heat tolerant, it has survived for many years. Plant nursery told us it was a Vinca, a plant not a climbing weed or creeper as I thought.
With recent rain, it has gone berserk, now almost out of control. It has a small blue flower, 5 petals, they look nice.
It has put down roots with every stem into the ground, mostly very hard to pull out. Good cross training, upper body strength of which I have not much.
Question ? How do I kill off most of this plant without killing everything else in the garden ? It's probably holding the fence up so I can't get rid of all of it.
Otherwise, an easy day, no sunshine, no rain, yet!!