Slovakia are looking to regain the attacking momentum that carried them to six successive wins, including victory against champions Spain, in qualifying for their first Euro finals since becoming an independent nation in 1993.
Resting key players ahead of a friendly with Germany on Sunday, the Slovaks struggled early to keep pressure on Georgia, who did not qualify for Euro 2016 and hired former Slovakia manager Vladimir Weiss in March.
Nemec, the team's second leading goal scorer in qualifiers, took advantage of his first opportunity, scoring from a fine pass from Matus Bero five minutes into the match.
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After the break, the 30-year-old striker for Dutch side Willem II Tilburg headed home a Lukas Tesak cross.
With two matches in three days, coach Jan Kozak tried out some newcomers looking for a spot in the Euro team, including Bero, who was making his first international appearance.
Adam Zrelak, earning his second cap, gave Slovakia their third goal in the 71st minute.
Georgia got one back moments later when Levan Kenia capitalised on a defensive mistake.
Slovakia face a tough task in France in a group with England, Russia and fellow Euro debutants Wales, teams all placed higher in the world rankings.
Kozak, in charge since 2013, has relied on a core group of players who helped Slovakia qualify for the 2010 World Cup, their only other major tournament appearance.
(Reporting by Jason Hovet, editing by Ed Osmond)
