Haaland's 25th goal helps keep Norway in Euro 2024 hunt
The striker struck on 25 minutes before captain Martin Odegaard doubled their lead eight minutes later as the home side dominated the match at Oslo's Ullevaal stadium.
However, with Norway needing all three points to remain in the hunt for one of the two qualifying spots from Group A, Budu Zivzivadze rattled the home side's nerves by pulling a goal back for Georgia in stoppage time.
Norway manager Stale Solbakken said his side posed a bigger threat as the game wore on.
"A slightly slow start, but at the same time we had full control. They laid very low and closed well. Then we gradually became more and more dangerous," he added.
"We have full control for a long time before they scored a little out of nothing."
Norway are third after five matches in the group, eight points behind leaders Scotland and two behind Spain, who have played one game fewer.