I haven't changed my rules since systemctl rudely barged onto the scene, so the last time I save mine I used "service iptables save".
I just went looking for the systemctl equivalent. The equivalents for start and stop are implemented, but not save.
But I found the old init.d script here: /usr/libexec/iptables/iptables.init.
I wonder why the didn't add something like this line:
ExecSave=/usr/libexec/iptables/iptables.init save
to this file:
/usr/lib/systemd/system/iptables.service
If that was done, I think this would work: systemctl save iptables.service