The world number one took her tally to 40 match wins and five WTA Tour titles in 2021 with a 6-3 6-1 victory.
Teichmann, ranked 76th in the world, had won all four of her meetings with top-10 players this season and accounted for Naomi Osaka, Karolina Pliskova and Olympic gold medallist Belinda Bencic during this exceptional week.
Beating Barty, however, proved a step too far. The Australian recovered from some early jitters, winning 85 per cent of points behind her first serve and breaking her opponent five times.
Teichmann's resistance faltered as errors saw her fall 5-3 behind in the opener and Barty won eight straight games to take command of the contest.
Barty needed just one match point to see out the victory, the first at Cincinnati by an Australian woman since Evonne Goolagong Cawley in 1973.
"I think being able to come through and play a really clean week and walk away with the title is probably not what I really expected of myself, but [it is] certainly nice," Barty, who did not drop a set all week, told the Tennis Channel.
Barty will be the firm favourite to win the US Open, where she has never before gone beyond the fourth round. The Flushing Meadows grand slam begins on Monday, August 30.