Egwene is a natural Dreamer and that ability is like Perrin's or Min's. It has nothing to do with the Power. While some of the Forsaken might share it, there is nothing to indicate Mesaana is one of them, and the Wise Ones themselves have been honing that skill for 3,000 years and see it as completely unrelated to channeling. Back in aCoS, I believe, one of the Wise Ones actually hypothesizes that the Wise Ones might know Tel'Aran'Rhiod better than the Forsaken. They trained Egwene in its basic principles so there is no reason why she could not theoretically be capable of defeating a Forsaken in a contest of dream-manipulation skills, particularly one like Mesaana, who is nowhere indicated to be especially skilled in the dream. It is no less improbable than Nynaeve defeating them in a poisoning duel or Rand in a sword fight, if they were able to get the Forsaken trapped in such a limited type of contest. A similar contest would be Nynaeve vs. Moghedian, pt 1, where Moghedia decided to confine herself to a contest of strength, where Nynaeve's own natural ability was sufficient to prolong the contest far beyond an abstract assessment of their assets and skills would lead you to expect. Likewise Egwene's own natural and inborn ability in Tel'Aran'Rhiod gave her an advantage over a woman channeling herself into the dream who did not have her practice and might have been handicapped by a Power-first mentality that limited her imagination in T'A'R.