The turning point came at 2-2 in the final set, when Ruud, who was playing in his first ATP Tour final, was unable to capitalize on three break point chances.
Garin broke in the next game by chasing down a drop shot and flicking a forehand winner.
Serving for the title at 5-3, the Chilean then hammered an ace to set up championship point. A heavy forehand on the next point decided the match.
The 22-year-old became the first Chilean to win an ATP Tour title since Fernando Gonzalez in Vina del Mar in 2009.
The victory was Garin’s second over the Norwegian in a month. He also defeat Ruud in the Brasil Open semi-finals.
Both players dropped serve twice in the first eight games of the match.
In the tiebreak, Garin, ahead 4-3, rifled a backhand return winner for the mini-break and went on to grab the advantage.
Ruud applied more pressure in the second set, finding the range on his serve and forehand, and eventually got a backhand error from the Chilean on break point to lead 3-2 en route to the set.
Ruud and his father, Christian, are the only Norwegian players to reach a final at this level.
Reporting by Gene Cherry in Raleigh, North Carolina; Editing by Peter Rutherford