First, tie the research to business goals. If the business goal is to increase adoption of the company’s product in a certain demographic, then emphasize the need to understand these users in order to properly message the value proposition of the product to them. It directly ties the value of such research to a bottom-line goal. Be ready to make a case on the ROI of such research.
Additionally, the need to understand these users in order to design for them is important to your design team, but is probably not a priority to the business. Emphasize this less than the bottom-line value the research will bring (as noted above).
Finally, use examples of how other companies use qualitative research, even if they are not in the same “business” as your company (though it works best if you can point to competitors doing such work). I have had great success in emphasizing case studies that I found from Google, Nike, etc. as an example to follow. Basically, demonstrate that other companies have succeeded using such techniques, and we can too! It’s almost a corporate version of peer pressure…