Synonyms for Upper hand:

n.

superiority, inside track, advantage, better, drop, over, vantage, bulge, jump, draw, edge. attribute (noun)
whip hand.
major advantage (noun)
edge, whip hand, superiority, advantage.
sway (noun)
advantage, dominion, superiority.
upper hand (noun)
whip hand.
vantage (noun)
vantage.

Other synonyms:

inside track, advantage. vantage. bulge. drop. advantage
edge.
Other relevant words:
better, vantage, superiority, dominion, drop, whip hand, jump, bulge, inside track, draw, advantage, edge.