Play was also halted for nearly three hours because of heavy rain.
When play resumed the Englishman took the second set, then couldn't manage to successfully serve for the match at 5-4 up in the third set. His nerves failed him and Golmard broke his serve to level at five games apiece.
However, Rusedski grabbed the advantage back in the very next game, breaking the Frenchman's serve.
The British player's nerve held in the 12th game of the final set, winning the game to love, and with it his 11th ATP tour title and around $100,000.
The two men now head to Melbourne for the Australian Open, which starts on Monday.
Rusedski, who will be seeded 28 in Melbourne, faces Aussie Scott Draper in his first round.
Golmard, who isn't among the 32 seeds for the Open, also plays an Australian, big-serving leftie Wayne Arthurs.
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