There are several ways we can find a biblical basis for the reduction in lifespans, at different levels from the literal to the literary.
At least in part, a biblical literal explanation is in Genesis 6:3, where God ordained that henceforth humans will not live beyond 120 years:
Genesis 6:3 (NIV): Then the LORD said, “My Spirit will not contend with humans forever, for they are mortal; their days will be a hundred and twenty years.”
A likely literary example can be found by comparing the lifespan of Adam, the first person in the Book of Genesis, with that of Joseph, the last person in the Book of Genesis. Adam is portrayed as living for 930 years, which is (30 x 30 + 30). Joseph is portrayed as living for 110 years, which is (10 x 10 + 10). The ancients were fascinated with numerology, and it could be argued that the biblical genealogies are literary examples of this.