No military victory could have been as valuable to them as the rift in the ranks of General Rashid Dostum, who has resisted the northwards advance of the Taliban since the autumn.
The defection to their side of General Abdul Malik, the Alliance's de facto Foreign Affairs minister, means that, at a single stroke, General Dostum has lost control of the areas to the west of his capital, Mazar- i-Sharif. This leaves his troops on the far western front hopelessly isolated; their defeat, which according to some reports is already a fact, would allow the Taliban to begin the final advance on Mazar, the key to the remaining third of the country not yet under their control.
Unlike the eastern front, the terrain the Taliban must cross is almost perfectly flat and an easy prospect for any mechanised army. They are already scenting victory. In a statement from Kandahar, the Taliban headquarters, Mullah Moham-med, the movement's reclusive leader, said that anyone surrendering voluntarily would be spared by the regime.
But he said: "Those forced to surrender by the Taliban will face Islam courts." No one in Mazar has forgotten what this meant for Mohammed Najibullah, the former Afghan president. On the fall of Kabul last September, the Taliban strung him up from a lamppost.
The routing of General Dostum has implications for the whole of central Asia. Mazar's population is already to swollen to many times its normal size by refugees from all over the country - some of them covert Taliban sympathisers, although many are not. The arrival of the fundamentalists, Western aid workers fear, could drive hundreds of thousands of refugees north across the borders of the central Asian republics.
The great worry is that sectarian warfare could spread. Tajikistan, which is only now emerging from a five-year civil war of its own, is seen as being particularly vulnerable.
General Dostum isn't finished yet, however. Mazar is still calm; he possesses a considerable number of tanks and fighters, and has been kept well supplied over the winter months by Russia, Iran and Uzbekistan, all of which are anxious to prevent Taliban's success.
General Dostum's current whereabouts are unknown. But if he can establish a second Western front, he may be able to survive. Much depends on the loyalty of his main ally in the east, the ethnic Tajik leader, Ahmed Shah Masoud; although last night there were unconfirmed reports of fighting in towns even to the east of Mazar.
Speculation as to what motivated General Malik, would-be architect of General Dostum's doom, is rife. Although his father, like General Dostum is an Uzbek, his mother is a Pashtun, the same ethnic minority as the Taliban. General Malik initially said his defection was for the sake of "national unity" and accused General Dostum of being a "bad muslim" and the main obstacle to peace; but such sentiments are suspiciously close to the official Taliban line to be given much credence.
He may simply have been bought - this has been one of the Taliban's most successful tactics in their 18 months advance across the country. Last year, one commander (who remains loyal to Dostum) was offered $11m (pounds 7m) to capitulate.
Still another theory is that General Malik is fighting a blood feud in the classic Afghan style. His family used to be headed by his brother, Rasool Palhawn, who rose to prominence as General Dostum's deputy. Last June, Mr Rasool was mysteriously assassinated by his bodyguard - on the orders, some say, of General Dostum himself. Mr Rasool was, some say, was simply getting too big for his boots. If the story is true, then General Malik has wreak-ed ample revenge.