מדרש על ברכות 17:24

(Devarim 16:6) "But to the place that the L-rd your G-d chooses — there shall you sacrifice the Pesach offering in the evening, etc.": R. Eliezer says: Towards evening (of the fifteenth of Nissan) you sacrifice it. When the sun sets, you start eating it. At the time of your starting to leave Egypt, (i.e., at midnight) you burn (what is left of) it.