Big Doc, starting up front, nodded home just six minutes from time to bag Ireland's first points of their qualifying campaign.
Stephen Carr also played as Damian Duff opened the scoring in the 18th minute only for Georgia to level on the hour via Levan Kobiashvili's free-kick.
Boss Kerr said: "It was an excellent performance, very disciplined and well structured, and overall I think we had the edge on them and deserved our victory."
However, events were overshadowed when an open penknife was thrown onto the pitch at the Lokomotiv Stadium, hitting Kevin Kilbane, and Doc was almost hit by a bottle as he celebrated the winner.
Simon Davies took another step towards a major final appearance as Wales marched on in Group Nine.
Simon filled an unfamiliar right-back role as Wales hammered Azerbaijan 4-0 at a packed Millennium Stadium.
The first goal, credited to Craig Bellamy, came after just 13 seconds and further goals followed from Gary Speed, John Hartson and Ryan Giggs.
The win leaves Wales in a strong position to qualify for the European Championship finals in Portugal next year, five points clear of Italy.
Gary Doherty grabbed a vital late winner against Georgia to keep the Republic of Ireland's Euro 2004 hopes alive.