Coming into the tournament, Vandeweghe had just one main draw win to her name all year, and when she dropped a tight first set and fell a break behind in the second this barren run looked all set to continue.
But after this uncertain start, Vandeweghe slowly grew into the match, finding her range on her fearsome serve and claiming the upper hand in many of the baseline exchanges.
"I think I broke her down a bit in the longer rallies - the longer the rallies went, the more confident I felt in being able to dictate the play and the points," Vandeweghe said.
An error-strewn service game from Bartoli allowed the American to draw level, and she was soon ahead, breaking twice more to level the match at one set apiece. Now well and truly in the ascendency, Vandeweghe consolidated her position with a break at the start of the decider before racing towards the finish line and a 46 63 61 victory.
"I go into every match and every tournament planning to win," she added. "But I've got to take it one match at a time. Winning today was a pretty big step for me as I've had a bit of a struggle at the start of the season and haven't had many wins, and today was really nice.
"The crowd support was great and it's a good feeling to be the underdog and have people cheering for you even if you mess up and miss a couple of easy ones."
Top seed Kerber has endured an up and down 2013 campaign thus far, but was far too strong for qualifier Samantha Crawford, who she defeated, 63 63.
"It was a tough one because it was my first round here and first matches are always dangerous," Kerber said. "But I think I played very well and felt good on court and I'm just happy to reach the second round now."
Kirilenko overcame a spirited first set showing from Mexican wildcard Ximena Hermoso to triumph, 75 61, while Ivanovic needed just 45 minutes to dispatch Marta Sirotkina, 60 60.