The Collaborative International Dictionary of English v.0.48:

Outface \Out*face"\ (out*f[=a]s"), v. t. [imp. & p. p.
   Outfaced (out*f[=a]st"); p. pr. & vb. n. Outfacing
   (out*f[=a]"s[i^]ng).]
   To face or look (one) out of countenance; to resist or bear
   down by bold looks or effrontery; to brave. --Shak.
   [1913 Webster]

         Having outfaced all the world.           --South.
   [1913 Webster]

WordNet (r) 3.0 (2006):

outface
    v 1: overcome or cause to waver or submit by (or as if by)
         staring; "He simply stared down his opponent" [syn: stare
         down, outstare, outface]