I imagine the magic of the Twili enhanced by the Triforce of Power granted to Zant from Ganondorf allowed for the creation of these things.
The Twili portals that the shadow beasts use to enter the light world in various locations. These are created just before several beasts enter a space to attack Link or take over a region. Even after their death there is no way to remove them. When Link has defeated the minions ans rescued the light spirit of the region, the portal remains. Meaning that it has an even greater power behind it than anything Link or the light spirits can bring against it. Which perfectly describes the Triforce of Power.
The banishment of the Dark Interlopers was actually done by the Light Spirits on command of the gods. Not the Gods themselves.
"It was then that the goddesses ordered us three light spirits to intervene. We sealed away the great magic those individuals had mastered." — Lanayru
Zant when he appeared before Lanayru showed that he was greater in power to Lanayru and could easily defeat it. As well as his breaking apart of all the light spirits into small tears of light then spreading twilight over their guarded regions of Hyrule. So the Triforce of Power Zant had access to gave him a higher authority over that of the Light Spirits and their power alone could no longer keep him sealed in the Twili Realm. As the triforce itself is a higher power than the light spirits, Zant was free to enter the light world if he wished and no authority could stop him. He had access to a greater power than what was used to seal the Twilight Realm, so he could easily break that seal.
However Midna as a Twili herself and very well versed in traditional Twili magic of the royal family can take advantage of the already created portals and use them when she wishes. She does not appear to be capable of creating them though, only using one that already exists.
I'll use my power to take you to the location of the open portal... Pick where you want to go." — Midna
The portals looking so traditionally Twili in appearance and Midna's capability of using them makes me believe that they are created through Twili magic but amplified by the triforce to a degree that they can return to the light world against the will of the Light Spirits that banished them centuries earlier. This would fall under the most basic definitions of power that the triforce piece represents.
- possession of controlling influence; "the deterrent power of nuclear weapons"; "the power of his love saved her"; "his powerfulness was concealed by a gentle facade"
- (physics) the rate of doing work; measured in watts (= joules/second)
- ability: possession of the qualities (especially mental qualities) required to do something or get something done; "danger heightened his powers of discrimination"
- office: (of a government or government official) holding an office means being in power; "being in office already gives a candidate a great advantage"; "during his first year in office"; "during his first year in power"; "the power of the president"
- one possessing or exercising power or influence or authority; "the mysterious presence of an evil power"; "may the force be with you"; "the forces of evil"
- exponent: a mathematical notation indicating the number of times a quantity is multiplied by itself
- might: physical strength
Showing that it might not instantly grant magical abilities to it's owner but greatly amplifies what magical abilities they do have to such a degree that they are superior to all others. Which is why Zant's magics continue to take on a Twili appearance.
Zan't breaking of the Mirror of Twilight was probably symbolic. He finally found the very item that was used to banish his people to an otherworldly prison centuries earlier. His breaking was both a final act of defiance against those would would punish his line eternally and a show that he was now a greater authority over it. That the Mirror would never be used against him ever again and that he was more powerful than those who judged his people. Anyone who actually saw the very same weapon used against their ancestors in such a way would likely act the same. They would want it removed or destroyed.