It is narrated from Sayyiduna Abdullah bin Abbas (may Allah be pleased with them both) that he said: I saw the Prophet (peace and blessings be upon him) eating the meat off a goat's bone; then he (peace and blessings be upon him) prayed, and he neither rinsed his mouth nor touched water.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الطهارة / 745
Sayyiduna Anas bin Malik (may Allah be pleased with him) said that the Messenger of Allah (peace and blessings be upon him) drank milk but neither rinsed his mouth nor performed ablution, and then prayed.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الطهارة / 746
Sa'id bin Jubayr (may Allah have mercy on him) said: I heard Ibn Abbas (may Allah be pleased with them both) say: If I were to eat bread and meat and drink she-camel's milk, I would not mind praying without performing ablution, except that I would rinse my mouth and wash the grease of the meat from my fingers.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الطهارة / 747