You can pipe a zip that contails a single sql file into mysql using -p flag with unzip.
unzip -p DUMP_FILE.sql.zip | mysql -u MYSQL_USER -p DB_NAME
Import/export MySQL using Gzip
Importing gzipped sql file into mysql
gunzip < DUMP_FILE.sql.gz | mysql -u MYSQL_USER -p DB_NAME
Use this for backing up MySQL to a gzip archive
mysqldump -u MYSQL_USER -p DB_NAME | gzip -9 > DUMP_FILE.sql.gz
NOTE: Make sure the zip/gzip archive file contains only a single sql file. Make sure to change DB_NAME to the name of your database on the MySQL server.
Import using SQL file
mysql -u MYSQL_USER -p DB_NAME < DUMP_FILE.sql