Brady did not drop a set all week on the way to her first WTA final and wore down Teichmann to claim the crown in a US Open tuneup event without spectators at Lexington, Kentucky.
“The sky is the limit so let’s keep going,” Brady said.
“There’s nothing better than playing at home in America, especially to win the title on home soil is a great achievement and something I’m going to be very happy about.”
The tournament was established in the wake of Covid-19 rescheduling issues as the first WTA event in the United States since the season was halted.
Brady, set to rise nine spots to a career-high 40th in Monday’s rankings, delivered the first finals defeat for 63rd-ranked Teichmann, who had won titles in 2019 at Prague and Palermo.
The two had split two prior matches, Teichmann winning in 2019 at Limoges and Brady winning last year at Cincinnati.
“Great battle as always,” Teichmann said. “Hopefully we’ll have many more in the future.”
Brady squandered a break chance in the fourth game with a backhand beyond the baseline and three more in the sixth game, twice on errant backhands.
Teichmann was denied on four break points in the seventh game, Brady saving with an ace, service winner and serve and volley winner and the Swiss hitting a forehand crosscourt return wide in the nine-minute game.
Brady, 25, finally struck for the break in the eighth game when Teichmann sent a forehand long, seizing a 5-3 lead, but the American squandered four set points in the ninth game before the 23-year-old Swiss netted a forehand to surrender the set after 55 minutes.
Teichmann, in her first WTA hardcourt final, sent a forehand long to give up a break in the opening game of the second set and Brady held six times for the triumph, ending matters after an hour and 42 minutes on a forehand winner.