The 37-year-old carded a five-under 66 on the third and final day in Zug, retaking the lead at 17 with her fifth birdie of a blemish-free final round and then parring the last.
Alexandra Forsterling - who chipped in for a remarkable par at 14 after her ball got stuck in a tree off the tee - shared second place on 12 under alongside Ireland's Anna Foster and Australia's Whitney Hillier, with Sweden's Kajsa Arwefjaell fifth on 11 under.
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Givens registered just one bogey all week, in her three-under opening round, with the Englishwoman also enjoying a five-under Friday, including three birdies on the trot to finish.
Her gains on Saturday came at two, three, seven and 10 ahead of picking up a decisive shot on the penultimate hole as she became the third English winner on the LET this year.
Charley Hull won the season-opening PIF Saudi Ladies International in February, while Esme Hamilton claimed a maiden title on the tour with victory at the South African Women's Open in April.
The next event on the calendar is the KPMG Women's Irish Open, from Thursday August 27, a tournament won last year by England's Lottie Woad while she was still an amateur.
Watch the KPMG Women's Irish Open live on Sky Sports+ from 2pm on Thursday August 27. Stream golf and more through NOW.
