The Gemara in Pesachim 105b establishes that one who recites a blessing must taste the wine over which he blesses, and Pesachim 106a clarifies that the cup of blessing requires a specific minimum measure — for once the wine falls below that measure, the cup is disqualified.
The operative minimum for drinking from the cup is described as מלא לוגמיו (a cheekful), which Shulchan Arukh, Orach Chayim 190:3 identifies as the majority of a revi'it; because every cup of blessing requires at least this amount, the Shulchan Arukh rules there that one should drink a full revi'it to avoid doubt about whether a concluding brachah is required, and Mishnah Berurah 296:23 confirms that the requirement for havdalah is precisely this measure of מלא לוגמיו.
The Rambam in Mishneh Torah, Sabbath 29:7 describes the one making kiddush as drinking מלא לוגמיו, and Maamar Mordechai Hilchot Shabbat, Chelek 1 16:118 draws from this that for both kiddush and havdalah alike, drinking מלא לוגמיו is sufficient to discharge the obligation.
Shulchan Arukh HaRav, Orach Chayim 296 rules that unlike kiddush, where those who hear the blessing must also taste the wine, for havdalah the one making havdalah customarily drinks the entire cup himself, and Kitzur Shulchan Arukh 96:7 codifies this practice, instructing that after concluding the brachah one sits and drinks the entire cup oneself.
Maamar Mordechai Hilchot Shabbat, Chelek 2 43:92 explains that the widespread custom not to pass the havdalah cup to the listeners is precisely in order to enable the one making havdalah to drink a full revi'it and recite the concluding brachah without doubt, and Maamar Mordechai Hilchot Shabbat, Chelek 2 43:94 adds that if the one making havdalah cannot drink a revi'it himself, he should taste a little and then have another member of the household drink the required measure.
Revavos Ephraim (Revavos Ephraim 8:216) discusses whether the obligation of drinking a cup of wine is fulfilled by drinking most of the cup rather than all of it, examining whether the obligation is tied to a specific measure or to completing the cup, and notes that the Rishonim link the mitzvah to drinking a full cup with its accompanying blessings.
Mishneh Halachos (Mishneh Halachos 8:33) addresses directly whether the havdalah wine must be drunk in one continuous gulp, surveying the Gemara in Sukkah and the positions of Rashi, Maharsha, the Taz, and the Magen Avraham on drinking wine in large gulps as an act of mitzvah, and concludes that drinking the havdalah wine in one gulp is permissible and constitutes fulfillment of the obligation — but stops short of requiring it.
