If you get a 1099-B then you do need to report the sale. The IRS will be looking for it. You might not get a 1099-B if this is a same day sale as brokers are not required to prepare a 1099-B in this case, but they are supposed to give you a "statement" that has the information you need if you do want to report the sale.
The way you eliminate the double income issue if you report the sale is to use the correct basis when you report the sale. The correct basis for the GROSS number of shares received - before any shares were sold or withheld for exercise or taxes - is the sum of what you paid for that gross number of shares plus the income created by your exercise or sale and reported to you on the W-2. If you aren't selling the gross number of shares all at once then divide that basis figure by the gross number of shares to come to a "per-share" basis number.
More likely than not the 1099-B doesn't report the correct basis as brokers are not required to do so. All they typically report is the "out of pocket" cost for the shares, omitting the compensation income element of the basis. So simply entering the 1099-B as it reads and not correcting the basis will have you reporting the income twice, once as compensation and then again as an overstatement of gain.
If the 1099-B is reporting the basis to the IRS and is not using the correct basis then enter the 1099-B as it reads on TurboTax's default 1099-B entry form but then click on the "I'll enter additional info on my own " blue button. On the next page enter the correct basis in the "Corrected cost basis" box. The correct basis is (number of shares sold) x (correct per share basis, which includes the compensation per share)
TurboTax will report the sale on Form 8949 "as reported by the broker" but will put an adjustment figure into column (g) of the Form, a code "B" into column (f) of the Form, and the correct amount of gain or loss which includes the adjustment.