The vote lineup in Eisenstadt v. Baird was very odd. The majority opinion by Justice Brennan was joined only by Stewart, and Marshall. Justice Douglas joined the majority opinion, but wrote that it was a First Amendment case. So the majority opinion (if you can call it that) only had four votes. Justices White and Blackmun concurred in judgment, based on a strained argument that the law couldn’t be applied to a married couple under Griswold: because “nothing has been placed in the record to indicate her marital status,” the conviction cannot be sustained. These two didn’t embrace Brennan’s reasoning at all. Chief Justice Burger dissented. So six votes to affirm the lower court, one to reverse. Finally, “MR. JUSTICE POWELL and MR. JUSTICE REHNQUIST took no part in the consideration or decision of this case.”
Eisenstadt was argued on 11/7 and 11/8 of 1971, and was decided on 3/22/72. Powell was confirmed on 12/7/71 and Rehnquist was confirmed on 12/10/71. Both began serving on 1/7/72. Had the case been argued about 2 months later, both Powell and Rehnquist could have participated–and potentially altered the fragile balance Brennan held together.
Based on a quick perusal of Oyez, the first case that both Rehnquist and Powell voted on was United States v. Mississippi Chemical Corporation. It was argued on 1/10/72 and decided on 3/6/72. They also voted on Argersinger v. Hamlin. It was initially argued on 12/6 (before their confirmation) but reargued on 2/28 (after they began service), so that’s kosher.
Roe v. Wade was argued for the first time on December 13, 1971 (after the confirmation), and was later reargued on October 11, 1972. Powell and Rehnquist voted after the latter argument.