Williams’ title defence came six years after Kim Clijsters completed her double.
“I’m so glad to be done here,” said Williams, who got a scare in a tight 53-minute opening set but easily won the second set. “I was glad to come here but it was tough.
“I flew from Wimbledon and had to get adjusted to the conditions and beat the jet-lag. I was glad to play and it’s great to win.
“But now I want to stay in the States for a while and prepare for the London Olympics.”
Williams defeated Vandeweghe in 90 minutes, hammering 21 winners, nine aces and getting four breaks of serve.