#CJam , 11 bytes

Thanks to @Dennis for two corrections and one byte off!

{1+_2f%1#<}

This is a code block (equivalent to a function; allowed by default) that expects the input array on the stack, and leaves the output array on the stack.

Try it online!

###Explanation

{ } e# define code block
 1+ e# attach 1 at the end of the array
 _ e# duplicate
 2f% e# modulo 2 of each entry
 1# e# find index of first occurrence of 1
 < e# slice before

CJam , 11 bytes

Thanks to @Dennis for two corrections and one byte off!

{1+_2f%1#<}

This is a code block (equivalent to a function; allowed by default) that expects the input array on the stack, and leaves the output array on the stack.

Try it online!

Explanation

{ } e# define code block
 1+ e# attach 1 at the end of the array
 _ e# duplicate
 2f% e# modulo 2 of each entry
 1# e# find index of first occurrence of 1
 < e# slice before

#CJam, 11 bytes

Thanks to @Dennis for two corrections and one byte off!

{1+_2f%1#<}

This is a code block (equivalent to a function; allowed by default) that expects the input array in the stack, and leaves the output array in the stack.

Try it online!

###Explanation

{ } e# define code block
 1+ e# attach 1 at the end of the array
 _ e# duplicate
 2f% e# modulo 2 of each entry
 1# e# find index of first occurrence of 1
 < e# slice before

#CJam, 11 bytes

Thanks to @Dennis for two corrections and one byte off!

{1+_2f%1#<}

This is a code block (equivalent to a function; allowed by default) that expects the input array on the stack, and leaves the output array on the stack.

Try it online!

###Explanation

{ } e# define code block
 1+ e# attach 1 at the end of the array
 _ e# duplicate
 2f% e# modulo 2 of each entry
 1# e# find index of first occurrence of 1
 < e# slice before

#CJam, 12 bytes

Thanks to @Dennis for a correction.

{~1]_2f%1#<}

This is a code block (equivalent to a function; allowed by default) that expects the input array in the stack, and leaves the output array in the stack.

Try it online!

###Explanation

{ } e# define code block
 ~ e# dump array contents
 1  e# push 1
 ]  e# pack into array: original array with an additional 1 at the end
 _ e# duplicate
 2f% e# modulo 2 of each entry
 1# e# find index of first occurrence of 1
 < e# slice before

#CJam, 11 bytes

Thanks to @Dennis for two corrections and one byte off!

{1+_2f%1#<}

This is a code block (equivalent to a function; allowed by default) that expects the input array in the stack, and leaves the output array in the stack.

Try it online!

###Explanation

{ } e# define code block
 1+ e# attach 1 at the end of the array
 _ e# duplicate
 2f% e# modulo 2 of each entry
 1# e# find index of first occurrence of 1
 < e# slice before