In many cases, you simply won't. There really are people like Dilbert's boss who run large departments, even large companies. Their lack of understanding of the business-critical nature of IT is exceeded only by their paltry management vision. The important thing is that you recognize when senior management is populated by such people. Then either hope the board gives them the boot, or get out yourself.
Managers love data and statistics.
IDC also named names, and the list of users included several venerable firms. That kind of background provides psychic support to get management on board with big, expensive projects. You must be realistic about the general image of the IT department at your company. Their managers report directly to the senior managers whose support you're trying to enlist. If that image is neutral or worse, you and your project are in trouble.