A time will come upon you in which none will be saved except one who supplicates like a drowning man

It is narrated from Sayyiduna Hudhayfah (may Allah be pleased with him) that he said: "A time will come upon you in which no one will be saved except the one who supplicates earnestly, as a drowning person supplicates."
This chain is sahih (authentic) on the condition of the two Shaykhs (Bukhari and Muslim), but the two of them did not record it in their books.

It is narrated from Ibn Zughb al-Iyadi that Sayyiduna Abdullah bin Hawalah al-Azdi (may Allah be pleased with him) stayed as a guest with him, and he said to me, while he was staying in my house: "May you be motherless (an expression of astonishment)! Is an annual stipend of a hundred (dinars) not enough for Ibn Hawalah?!" Then he related that the Messenger of Allah (peace and blessings be upon him) sent us on foot around the outskirts of Madinah to obtain spoils, but we returned having obtained nothing. He (peace and blessings be upon him) saw the signs of hardship on our faces, so he (peace and blessings be upon him) stood among us and made this supplication: 'Allahumma la takilhum ilayya fa-ad'ufa 'anhum, wa la takilhum ila anfusihim fa-ya'jizu 'anha, wa la takilhum ilan-nasi fa-yasta'thiru 'alayhim' (O Allah, do not entrust them to me, lest I be too weak to provide for them; nor entrust them to themselves, lest they be incapable of it; nor leave them at the mercy of people, lest they claim precedence over them). Then he (peace and blessings be upon him) said: "You will certainly conquer Syria and Persia (or Rome and Persia), until one of you will have so many camels and so many cows, and until a man will be given a hundred dinars and will be displeased with it (considering it little)." Then he (peace and blessings be upon him) placed his hand on my head and my forehead and said: "O Ibn Hawalah, when you see that the caliphate has descended upon the Holy Land (Bayt al-Maqdis), then be certain that earthquakes, afflictions and great trials have drawn near. On that day the Hour will be closer to the people than this hand of mine is to this head of yours."
This hadith has a sahih (authentic) chain of narration, but the two Shaykhs did not record it, and Abdur-Rahman bin Zughb al-Iyadi is one of the well-known Tabi'un of Egypt.