WordNet (r) 3.0 (2006):

drink up
    v 1: drink to the last drop; "drink up--there's more wine
         coming" [syn: drain the cup, drink up]

Moby Thesaurus II by Grady Ward, 1.0:

61 Moby Thesaurus words for "drink up":
   absorb, adsorb, assimilate, bib, blot, blot up, booze, chemisorb,
   chemosorb, digest, drain the cup, dram, drink, drink bottoms-up,
   drink deep, drink hard, drink in, drink off, drink to, engross,
   filter in, follow strong drink, gargle, grog, guzzle, imbibe,
   infiltrate, knock back, lap, lap up, nip, osmose, percolate in,
   pledge, pull, quaff, seep in, sip, slurp up, soak, soak in,
   soak up, sorb, sponge, sponge up, suck, suck in, suckle, sup, swig,
   swill, swill up, take in, take up, thirst, tipple, toast, tope,
   toss down, toss off, wash down