They can overturn it by amending the constitution to ensure the rights of a fertilized egg are legally fully equal to the rights of the woman whose uterus it needs to use to develop. In Roe vs. Wade the court decided a woman's right to privacy is violated by abortion restrictions. A constitutional amendment would attempt to place the right to life of a blastocyst on a higher level than the mother's right to privacy, and the court would have to interpret future cases in this light, effectively overturning Roe vs. Wade.
Something just occurred to me: I don't know all the details of Roe v. Wade, but striking down the idea that the right to privacy trumps the right to life. I can think of many "national security" scenarios where it could be lives are being saved. Does that mean that the government should be free to wiretap you, for instance?