In the Wheel of Time the "Superboys" (Rand, Mat and Perrin), all exhibit quite extraordinary close-combat prowess, although neither of them fought before the start of the books. For Rand and Mat it is explained quite well: Rand has Lews Therin's memories seeping through, who was a blademaster for all practical purposes and he trains for hours every day. Mat has the memory of thousands soldiers, all at the ready. But Perrin's extra skill is being a Wolfbrother which I guess adds some edge, but he is outnumbered by Aiel at Dumai's Well, the Aiel who are in general the best fighters around. So, how does he not get skewered by an Aiel spear?
I do not believe that it's ever overtly explained, but I would argue it's a bit more of a combination of factors with Perrin.
Leaving aside plot armor, Perrin certainly started off as the most physically imposing of the three: after years of apprenticing for a master blacksmith, he was described in the early books as being uncommonly strong.
Add to that enhanced wolf senses and ta'veren luck, both of which help him avoid getting stuck unprepared; certainly a factor in mass combat.
Finally, he has seen a share of battles by this point in the story, in his own life, including against seemingly hopeless odds (e.g. the Battle of the Two Rivers). He has been stuck in the middle of situations that would make anyone grow up quickly if they survive.
Perrin aside, it's worth noting that the Aiel in this scene are not in the best position to start with. Perrin's forces hit them hard and by surprise. They engage Wise Ones to use the One Power for the first time. Aiel are used to light infantry tactics (hit and run, surround your enemies, as described by Lan and Ituralde in various places) and here they're being caught between a rock and a hard place even before the Ashaman show up. They're not at the top of their game, is my point. They are dealing with charging cavalry and lightning from the sky. As skilled as the Aiel are, they're not superhuman, and they can be broken.