Wozniacki had to negotiate her way past this year's Wimbledon runner-up Sabine Lisicki in the semi-finals while a retirement from Swiss semi-finalist Stefanie Vogele put Beck, who was a set up, through.
The former world number one made light work of Beck in just one hour and 14 minutes to take the 21st title of her career.
At the Kremlin Cup, Simona Halep stunned Sam Stosur 7-6(1) 6-2 to win the tournament.
Stosur, a runner-up in Moscow last year, saved 11 break points in the first set but Halep prevailed in the tiebreaker.
Halep raced into a 4-1 lead in the second before sealing the win on her first match point.
"I've been playing more aggressively this year, hitting the ball very strong, and I'm more relaxed on the court and have been focusing much better on every point," Halep said.