In a game that goes to time and is tied, if I add prizes to my opponent's field with Palkia & Dialga LEGEND's "Time Control" attack on my next turn, do I win?
Yes. After regulation time (plus any additional turns) is completed, once you have fewer prizes remaining than your opponent, you win.
Source: Triumphant FAQ (2010-11-04), PUI Rules Team (2010-11-04)

Relevant cards

Note: All applicable cards may not be listed below.
HGSS4_101
HGSS4_102