The Megillah says that they established "these days" (of Purim) as days of feasting and celebration. The Rambam says that we fulfill the obligation by becoming intoxicated. The Lubavitcher Rebbe says that since the days were established as days of feasting, it's possible to say the obligations of feasting (including intoxications) apply the whole holiday.
The Rambam (Megillah 2:15) writes:
What is the nature of our obligation for this feast? A person should eat meat and prepare as attractive a feast as his means permit. He should drink wine until he becomes intoxicated and falls asleep in a stupor.
The Lubavitcher Rebbe, in Likutei Sichot Vol 7 (translated here) discusses the connection between "Ad D'lo Yadah" and Purim. From there (chapter 2):
The obligation to become intoxicated on Purim [has its source in the Megillah's description of the celebrations as] "days of feasting and celebration." "Becoming intoxicated" reflects the manner in which the feast must be held.
It is possible to explain that the mitzvah of "feasting and celebrating" is distinguished from all the other mitzvos ordained by our Sages to be observed on Purim in that the obligation to observe this mitzvah applies during every moment of the festival of Purim. The observance of the other mitzvos of the day, by contrast, [is associated with a specific time]
With regard to feasting and celebration, by contrast, since the Megillah describes the days of Purim as "days of feasting and celebration" - and "feasting and celebration" is stated directly after the term yimei ("days of"), (in contrast to "sending gifts of food and gifts to the poor" which is stated afterwards), it is possible to explain that the obligation to feast and celebrate applies every moment of the day. [The fact that we do not spend the entire day "feasting and celebrating" can be explained as follows:] Through observing the mitzvah once during the day, its observance is extended throughout the entire day.