The 36-year-old Williams came from a set down to win the match 6-7(3) 6-2 6-3 to become the first player into Saturday's final, where she will meet younger sister Serena after she later routed Mirjana Lucic-Baroni 6-2 6-1.
The defeat was tough to take for Vandeweghe, whose temper has been known to manifest itself upon her racquets, though they survived on Thursday.
"Straight after the match I was pretty upset," Vandeweghe told reporters. "I had a feel-sorry-for-myself moment.
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"What made me feel a lot better was when my team came over when I was in the gym sitting by myself, they came over, gave me a big hug.
"Each and every one of them told me how proud they were of how I competed out there and everything like that. So that kind of picked me up and made the situation feel a lot better."
Despite Thursday's loss, Vandeweghe could be pleased with her tournament.
She knocked out world number one Angelique Kerber, French Open champion Garbine Muguruza and former grand slam finalists Roberta Vinci and Eugenie Bouchard.
Her powerful game raised a level with every round she advanced and she is also projected to crack the top-20 for the first time, rising from a pre-tournament ranking of 35.
"I'm very happy with starting the year this way, putting validation to the hard work that I've put in, in the off-season, the sacrifices, all the good stuff like that," she added.
"But at the same time I'm not satisfied. I think that's a good thing."
Not being satisfied undoubtedly comes from the impact of her sporting family.
Her mother Tauna swam for the U.S. at the 1976 Olympics, while grandfather Ernie and uncle Kiki played in the NBA, and Vandeweghe had said earlier that no-one gave each other any latitude when it came to intra-family sporting contests.
Williams was equally as ruthless during their match, winning the crucial points when Vandeweghe felt like she was within a sniff of staging a fightback.
"In the second set, she definitely changed how she was playing," she said. "I wasn't as quick to counteract that. But she also came up with some clutch plays.
"It's a combination of myself not playing as well to get back into the match. But you have to give credit where credit's due, (she) played better than I did today when it mattered."
(Writing by Greg Stutchbury in Wellington; Editing by John O'Brien)
