Towers, trailing 30-28 after a first half which was marked by a string of missed shots, opened the second period with a trio of three-pointers from Paul Deppisch and soon led 44-32.
On Tuesday night the Group H leaders, Verona of Italy, beat Podgorica, of Yugoslavia, 85-75 and Turkey's PTT Ankara defeated the Hungarians Marc Kormend 93-81. London's win leaves them one point behind the Turks and the Hungarians, who they must play in their two remaining away games, and a point clear of Tbilisi and Podgorica who visit Wembley in three weeks time.
London's victory bore their trademark of physical, intimidating defence as Karl Brown, Danny Lewis and the substitute Martin Gottfried smothered the Georgian back court and forced a succession of turnovers.
Joe Hooks, who scored 17 points, and Neville Austin, with 11, gave London a sharp edge around the Georgian basket. Brown, with 15 points, and Lewis and Deppisch, with nine each, added the outside threat.
Derby Storm's Mike Gonda, the fourth-highest three-point shooter in the Budweiser League, has walked out on the club to join his wife in the United States.