He did not. Rather, he wrestled with the angel that was sent by God. It happened at the banks of the Yabok stream (Genesis 32).
God sent a mysterious messenger to wrestle with Jacob one night (Genesis 32:25). Tradition states that it was an angel in human form; the guardian angel of Esau (Rashi commentary, quoting the Midrash). The angel's task was to attempt to spiritually blind Jacob (K'li Yakar commentary, ibid), but Jacob prevailed (Genesis 32:26-29), and because of that, he was renamed Israel. At first the angel conferred the new name (Genesis 32:29), and later, God also did (Genesis 35:9-12).
Note that the Word Elohim, in the text, often refers to things other than God, such as judges (Exodus 21).
Isaac's son, Jacob was left alone and wrestled with an opponent all night until the break of day, when the man said he must leave (Genesis 32:24ff). Even though his leg was dislocated, Jacob refused to let his opponent go unless he blessed Jacob.
That the 'man' was a god is amply demonstrated - Jacob asked for his blessing, he had the prerogative of changing Jacob's name, Jacob's new name was Israel (generally assumed to mean 'wrestled with God') and Jacob called the place Peniel ('the face of God') because he had seen God face to face. If the man who wrestled with Jacob was a god, then Jacob was also a god in a much earlier tradition behind this passage, as demonstrated by the fact that he was such an even match for his opponent. And if the opponent was a god, he was also a sun god - daybreak signalled the end of the contest, he had to leave Jacob before the sun could rise, then the sun rose upon Jacob. This is consistent with the ancient daily struggle in which the sun god defeats the moon god at dawn.
The name of the place Jacob wrestled with God is right there in the text. It is Peniel.
