Washington once said that during the Revolution the British beat them all the time, but that the Colonial Army won the two battles that counted....

If I had to venture a guess, I would say that Washington
was referring to the Battle of Saratoga in 1778, and the Battle of Yorktown in 1781. 
You're right, there were other battles the Americans won, but these two had very
significant impacts on how the war would and could be waged by the Colonials, and on the
outcome of the war itself.

Saratoga, it could be argued,
was the first time the American Army had fought a traditional, open field battle against
the British and won it on their own terms.  This helped the diplomatic efforts of
Benjamin Franklin to secure the Treaty of Alliance.  This led to offers of training and
financial aid (loans) for the war, as well as threw the French Navy into the
fight.

Yorktown was the decisive battle of the war and the
one which gave America its independence.  General Cornwallis of the British was cornered
against the ocean, and thanks to the French Navy, the British Navy could not come and
rescue his forces.  He was forced to surrender, the first time an entire British Army
had done so.  This virtually guaranteed American independence, and could be called
Washington's greatest moment as commander.