It is also possible to decompress it using standard shell-script + gzip, if you don't have, or want to use openssl or other tools.
The trick is to prepend the gzip magic number and compress method to the actual data from zlib.compress:

printf "\x1f\x8b\x08\x00\x00\x00\x00\x00" |cat - /tmp/data |gzip -dc >/tmp/out

Edits:
@d0sboots commented: For RAW Deflate data, you need to add 2 more null bytes:
→ "\x1f\x8b\x08\x00\x00\x00\x00\x00\x00\x00"

This Q on SO gives more information about this approach. An answer there suggests that there is also an 8 byte footer.

Users @Vitali-Kushner and @mark-bessey reported success even with truncated files, so a gzip footer does not seem strictly required.

@tobias-kienzler suggested this function for the bashrc:
zlibd() (printf "\x1f\x8b\x08\x00\x00\x00\x00\x00" | cat - "$@" | gzip -dc)

zip is a file format that wraps header and trailer information around compressed data streams in order to represent a set of files and directories. The compressed data streams are almost always deflate data streams, which can in fact be generated and decoded by zlib. zlib also provides the crc32 function which can be used to generate and check the crc values in the zip wrapper information.

What zlib does not do by itself is decode and deconstruct the zip structure. You can either write your own code to do that using the specification (not very hard to do), or you can use the minizip routines in the contrib/minizip directory of the zlib distribution, which provides functions to open, access, and close zip files.