Saratoga

So while the British were being repelled at Ft Stanwix in western NY, General Burgoyne and 8000 British troops and German Hessians had taken Ft Ticonderoga and were advancing down the Hudson River. General Gates dug in his colonial army near Stillwater under the direction of Kosciusko, his Polish engineer who did so much for the American cause (and is a truly unheralded hero).
The British were bottlenecked and fought an initial action on September 19, 1777. While the redcoats won the field, they sustained numerous casualties and didn't skirt colonial defenses. Benedict Arnold is largely responsible for the strategic success of the battle and may have ultimately defeated the British that day if he were not at odds with Gates.
Burgoyne dug in hoping for reinforcements from NYC. By Oct 7 his troops were hungry and tired. He attempted a reconnaissance in force and foraging effort on the American left flank which resulted in a pitched battle with the militias guerilla tactics and marksmanship eventually driving the British back to their redoubts and finally into full retreat under darkness.
Arnold was again instrumental in leading colonial forces, even though he had been effectively stripped of his command by Gates earlier. A monument on the battlefield shows where Arnold fell, his leg shattered by a ball. But it bears no name because of his later treachery.
British strategy to split New England, the home of the rebellion, from the other colonies had failed. Critically, the American victory over the British army, the most powerful in the world, brought the French into the war. The only mention in textbooks these days is that Saratoga was the turning point with maybe a date and a few names - likely less than I just wrote.
I mentioned the division in the Six Nations previously. The Oneida and Tuscarora sided with the colonies while the Mohawk, Cayuga, Onondaga, and Seneca joined the British. All played critical roles as combatants and scouts. The split had long term effects on the Nation as well.

Capture of British artillery was crucial to the colonial effort. 

Saratoga has some of the best 3D models in the country.