The Torah tells us that Yitzchak davened to Hashem opposite his wife because she was childless, and that Hashem then accepted the Tefillah of Yitzchak, and Rivkah conceived (בראשית כ"ה:כ"א). According to the Pirkei DeRabbi Eliezer (פרק ל"ב), Yitzchak took his barren wife to pray with her on Har HaMoriah, which had been the precise location of Akeidas Yitzchak many years earlier. We can make several comparisons between this event and the Akeidah. According to Rashi's comment on this Posuk (שם בד"ה לנכח), the report that Yitzchak davened "opposite his wife" means opposite in the sense that he stood in one corner and she stood in another while they both prayed. This is an example of teamwork here; Yitzchak and Rivkah both knew their mission and what they were praying for. They were thus two people pursuing the same goal. This is comparable to the trip taken by Avraham and Yitzchak on the way to the Akeidah, where the Torah tells us "וילכו שניהם יחדיו," "the two of them walked together" (שם כ"ב:ח'). Rashi (שם) explains that even after Yitzchak understood that he was going to be sacrificed, he walked together with Avraham. They too thus went together to Har HaMoriah because they both understand their mission; they were on the same wave-length and were both aware of what would transpire.
Furthermore, prior to going up onto Har HaMoriah, Avraham told the נערים, the lads who accompanied him on the journey, "שבו לכם פה", "you stay here" (שם פסוק ה'). Obviously, what was to transpire on the mountain was something between only Avraham, Yitzchak and Hashem. Here too, in our Parsha, what transpired with these Tefillos was between Yitzchak, Rivkah and Hashem; the ones who were left out of the picture here were the evil members of the family of Rivkah, mentioned in an earlier Posuk (שם כ"ה:כ') Finally, we know that Hashem came through for Avraham at the Akeidah, telling him not to harm Yitzchak in any way (שם כ"ב:י"ב). Similarly in our Parsha, Hashem came through for Yitzchak "and Rivkah his wife conceived" (שם כ"ה:כ"א).