The posterior one-third of the tongue is drained by the **basal vessel**, which is a lymphatic vessel arising from the base of the tongue. It drains into the jugular lymph nodes. The marginal vessel drains the lateral surface, the central vessel drains the midline, and the lateral vessel is not a recognized lymphatic vessel in this region. The basal vessel is specifically responsible for draining the posterior third of the tongue.

**✓ Correct: A. Basal vessel**