A single break in the first game of the match was enough for Stephens to win the first set, and the American led with a break at 3-1 in the second.
Robson, who at 53 is ranked 15 places beneath her opponent, fought back to take the set into a tie-break, but Stephens prevailed in the final tournament before the Australian Open.
There were missed chances for Robson, who had six break-point opportunities in the match, including four in the first set.
British number one Heather Watson withdrew from the tournament because of injury.
Belarusian Olga Govortsova caused an upset in the first round with a comfortable straight-sets win over Spain's Carla Suarez Navarro.
The fifth seed, ranked 34 in the world, was defeated 6-2 6-1 by a player ranked 57.