Karla Five's ship accidentally entered our universe while it was in the vicinity of Amphion, a nova in the antimatter universe that was becoming a star. While studying Amphion, the ship was pulled in and crossed through a gateway and emerged in our universe near the Beta Niobe supernova. The ship was able to travel at speeds of warp 36 which had allowed it to survive the heat of a supernova.
Karla Five returned to her own universe by re-entering the Beta Niobe supernova, but it also brought along with it the USS Enterprise. Captain James T. Kirk had ordered his crew to engage the tractor beam on Karla Five's ship as it was heading directly into the supernova and he feared for the life of its sole occupant, Karla Five. Unable to disengage the beam, the Enterprise passed through the gateway between the two stars and entered the antimatter universe, just seconds behind Karla Five's ship.
The vessel, despite its speed and power, was only able to accommodate a few people and was nowhere near the size of the Enterprise. Still, the Enterprise was able to return to its own universe by being towed by Karla Five's ship into another nova in the antimatter universe. (TAS episode: "The Counter-Clock Incident")