Most lenders lend on the lesser of appraised value or purchase price. They do this to protect themselves from fraud and overlending on a property. The theory goes that if the purchase price is less than the appraised value then the appraised value is overestimated.
as long as a the appraisal is legitimate with comparable properties to back it up you can do what you are looking to do. As long as the seller your broker and even your r/e agent is willing to credit back money to you at closing it is definitely possible.