But reluctant to commit its own troops, the U.S. allowed Osama bin Laden to escape from the Tora Bora mountains, reports CBS News chief foreign affairs correspondent Lara Logan.
Then came what many here see as the gravest error of all: Afghans were wary as the U.S. turned its attention to invading Iraq - and they were right. Everything from reconstruction and aid to the fight itself suffered as the U.S. shifted its resources and its focus away from Afghanistan and the commitment it had made to the Afghan people.
Not surprisingly, Afghan support for the war began to fade.
CBS News Special Report: The Road Ahead
Logan asked Afghan President Karzai's main rival Abdullah Abdullah what was lost in Afghanistan with the U.S. focusing on Iraq.
"The greatest opportunity, the best opportunity for the stabilization of Afghanistan," Abdullah said.
That lost opportunity has led the U.S. into a fight that would have been unimaginable eight years ago when the Taliban collapsed in disarray.
Back then valleys in northeastern Afghanistan were peaceful; the U.S., believing their enemy was defeated, put few military assets on the ground.
Another grave mistake.
Now, even the most remote mountains are killing grounds for determined Taliban and al Qaeda fighters - no longer afraid to stand and fight whenever they choose.
Year after year, the U.S. blindly claimed success and failed to adjust its strategy or admit its enemy was getting stronger.
The fighters it faced became proficient in small unit tactics which they learned from studying the U.S.
That can be seen in a Taliban propaganda video, which shows how the Taliban execute an attack on a small U.S. combat outpost.
Loaded with ammunition, Taliban fighters climbed to the highest reaches of the mountains. They began their assault before first light, using the type of overwhelming fire usually used against them by the U.S.
Their commander is so certain of victory that he orders his fighters to open fire on the jets when U.S. air support is called in.
"Taliban stay in your places!" he commands. "If the jet comes down again, shoot the wings!"
With a huge fire raging, the Taliban wait for survivors to stumble out. Twelve Afghan soldiers are captured, three U.S. Marines killed.
The U.S. counter-attacked and three days later the abandoned post was recaptured.
But forcing an American withdrawal was a victory for the Taliban - a sign of how far they have come since the U.S. thought they were defeated.
"Defeat is a very strong word," Col. James Kraft said. "Will you ever defeat an insurgency in total? It's a challenge. I think you've got to get it to a moderate level of chaos, a level that's accepted."
An acceptable level of chaos may not be what the U.S. went to war in Afghanistan hoping to achieve. But it may be how success is measured, if it's enough to stop al Qaeda from threatening the U.S. again.
More special coverage on CBSNews.com:
Marines in Afghanistan: A Day in the Life
Taliban Gaining Firepower and Confidence
Battle of Wanat - Inside the Ambush
Afghanistan, 8 Years In: How We Got Here
McCain, Kerry Answer Key Questions on Afghanistan
Public's Views of Afghanistan War Have Turned Sour