The Spanish estremecer (“to shake”) comes from the Latin prefix ex– (which more commonly means “out of”, but can also add emphasis, as in “thoroughly”), with the Latin verb tremere which means the same: “to shake”.
From the same Latin root, we get the English… tremors. That is when the earth shakes, after all?
We can see the tr-m root clearly in both the Spanish and English words. But it’s easy to miss because of the misleading es prefix!