Now you're thinking with plumbers.
While Portal and Portal 2 are certainly puzzle games at heart, their objective is that of the platformer: Get from Point A to Point B. Of course, if the Mario Brothers had had access to Chell's Aperture Science Portable Quantum Tunneling Device, the fight against Bowser would have been much easier.
This video from Dorkly shows just how the classic platformer Super Mario Bros might have gone if Mario and Luigi had been thinking with portals.
Poor Bowser didn't stand a chance.
This, of course, only leads to further speculation - like what would have happened if Cloud had used one giant portal gun to make sure Sephiroth's Meteor spell would just come out the other side of the planet when it hit. Or if M. Bison could be made to fly through the air in an eternal Psycho Crusher attack.