WordNet (r) 3.0 (2006):

upper hand
    n 1: position of advantage and control [syn: upper hand, whip
         hand]

Moby Thesaurus II by Grady Ward, 1.0:

83 Moby Thesaurus words for "upper hand":
   advantage, ascendance, ascendancy, authority, balance of power,
   bulge, charisma, charm, clout, coign of vantage, consequence,
   control, credit, dominance, dominancy, domination, dominion, drop,
   edge, effect, eminence, eminent domain, enchantment, esteem, favor,
   flying start, force, good feeling, head start, hold, importance,
   incidental power, influence, influentiality, inside track,
   insinuation, jump, leadership, leverage, magnetism, mastery,
   moment, odds, overlordship, personality, persuasion, potency,
   power, predominance, predominancy, predomination, preeminence,
   preponderance, prepotence, prepotency, pressure, prestige, primacy,
   principality, purchase, reign, repute, rule, running start, say,
   something extra, something in reserve, sovereignty, start, suasion,
   subtle influence, suggestion, superiority, supremacy, suzerainship,
   suzerainty, sway, vantage, vantage ground, vantage point, victory,
   weight, whip hand