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#[MATL](https://github.com/lmendo/MATL), 6 bytes

 toYs~)

[__Try it online!__](http://matl.tryitonline.net/#code=dG9Zc34p&input=WzQyLCAxNCwgNDIsIDQzLCA0MSwgNDA4MDYyMiwgMTcxNDgwMzcyXQ)


###Explanation

 t % Input array implicitly. Duplicate
 o % Parity of each entry. Gives 0 for even entries, 1 for odd
 Ys % Cumulative sum
 ~ % Logical negate. Gives true for the first run of even entries, and then false
 ) % Use this as logical index into the original array. Implicitly display

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