Rising interest rates should make it difficult to roll-over debt, and should restrict credit creation which should reduce the rate of growth in the money supply. The income received on savings (interest income) should act more like a transfer, from borrower to lender, than creation of money.
The rising interest rates of the early-1980s, coinciding with large federal government budget deficits, should have reduced the creation of credit and driven down the rate of inflation.
Indeed, inflation did begin to decline starting in the early-1980s, and inflation and interest rates began a long-term decline - eventually reaching deflationary levels as interest rates dropped toward zero. There were even negative real interest rates in the late-1970s and early-1980s.
Interest rates (red), affected by demand for savings relative to supply; and inflation (blue), a consequence of credit creation.