If a miracle makes sense to a secular world it ceases to serve it's purpose.
When we encounter someone who does not believe in miracles (and who we wish did believe) it is tempting to rationalize them and attempt to show how they are really quite reasonable, to work from what we know that our listener already believes in and hope to piggy-back miracles onto something already held. We do this hoping to convince the listener that miracles should be believed in just like the thing we piggy-backed upon. However, to pursue this course may end up being counter-productive to our purpose.
I don't deny that there are some cases when this piggy-backing might work, like if the listener were already comfortable and conversant in actions of higher powers and metaphysics it's not a big step from there to Jesus healing as in the Gospel stories or healings taken as the intercession of saints. (It's more of a horizontal expansion than a vertical step, not so much something new as exposing more of what was already possessed.) Where it perhaps isn't a good idea, for example, is trying to step them up from a viewpoint of materialism to miracles by using the ideas and language of materialism to explain miracles. This method seems more likely to lower miracles to that person's materialism rather than elevate their materialism to an understanding of miracles.
The late Cardinal Avery Dulles, in his book The Craft of Theology says "The whole point of miracles...is that they are beyond what we would have deemed possible. They shake us up and bewilder us, so that we acknowledge that our previous horizons were too narrow". Miracles are meant to break our expectations so we must resist the temptation to define them only within the terms of our expectations.
Miracles must supersede the secular world-view because the whole point of miracles is to point us to the transcendence of God, God who doesn't fit into the secular view.