Musannaf Ibn Abi Shayba 3:4305

Abu Usama narrated to us, from Yahya ibn Maysara, who said: Al-Ala ibn Badr narrated to us, from the one who heard Salman say: "Beware of staying up late at the beginning of the night, for it is a destroyer (or a waster) of its end. So whoever does that, let him pray two rak'ahs before he goes to his bed."