<Page>

                                                                    EXHIBIT 32.1


                            CERTIFICATION PURSUANT TO
                             18 U.S.C. SECTION 1350,
                             AS ADOPTED PURSUANT TO
                  SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

     In connection with the Annual Report of EXACT Sciences Corporation (the
"Company") on Form 10-K for the period ending December 31, 2003 as filed with
the Securities and Exchange Commission on the date hereof (the "Report"), I,
Don M. Hardison, Chief Executive Officer of the Company, certify, pursuant to
18 U.S.C. Section 1350, as adopted pursuant to Section 906 of the
Sarbanes-Oxley Act of 2002, that:

(1) The Report fully complies with the requirements of section 13(a) or 15(d) of
the Securities Exchange Act of 1934; and


(2) The information contained in the Report fairly presents, in all material
respects, the financial condition and result of operations of the Company.


/s/ Don M. Hardison
- ------------------------
Don M. Hardison
Chief Executive Officer
January 29, 2004