I believe the Mace did really overpower Palpatine and win the duel. Palpatine may have been a sith lord, but he was weak, obviously no match for one of the strongest jedi in the order. However, as stated above, Anakin wanted Palpatine alive so he could learn the powers to save Padame. If Anakin had not arrived when he did, Palpatine would have died. Palpatine tried to play the sympathy card and make it look like he was just a helpless old man.
Long story short, Mace Windu should have won this duel. George Lucas is just trying to confuse us.