You definitely want to report both the K-1 and the 1099-B. A partnership does not pay taxes at the partnership level. Instead, they pass all their taxable information down to the partners themselves (you) and you have to pay the taxes. So you do that by reporting everything in the K-1 section of the TT interview.
In addition, the partnership reporting will change your cost basis for the 1099-B. The info you got from the broker is likely incorrect (because they don't know what the partnership reported). You'll have to adjust the cost reported on the 1099-B.
Finally, be aware that you have to watch out for double-reporting the sale. This longer thread goes into more detail about some of the pitfalls, and how to make sure you only report the sales once: https://ttlc.intuit.com/community/investments-and-rental-properties/discussion/how-i-report-the-sale-of-mlp-shares-in-turbo-tax-i-sold-all-shares/00/776624