It is not an outcome anybody expected, least of all Saddam Hussein, the Iraqi leader, who probably calculated that by sending his tanks into Arbil, the Kurdish capital, two weeks ago, he would save Mr Barzani from defeat and keep the civil war going. This would have enabled him to be the ultimate power broker in Kurdistan, gradually increasing his influence by playing the two Kurdish parties against each other.
The most important change in the political map of Iraq and Kurdistan since the start of the month is that, to the surprise of all, this did not happen. There is now only one Kurdish leader and party left. Driving through Kurdish village there is scarcely a tumble-down hut which has not sprouted the yellow flag of the victorious Kurdistan Democratic Party KDP. Equally telling, the price of a Kalashnikov machine gun in the market has more than halved to between 300 and 400 Iraqi dinars (pounds 8 to pounds 10) since the beginning of the month as thousands of PUK militiamen try to get rid of their weapons.
Even after the fall of Arbil on on 31 August, there was no reason why Jalalnal Talabani's PUK forces, still holding the city of Sulaimaniyah and many other towns and villages, should not have fought on. "They held positions from which they could have held us off by throwing rocks," said one KDF member. Overall, Mr Barzani, told The Independent in an interview, his forces lost 150 dead and 500 wounded in the war.
The main reason for the rout was that the PUK, desperate for the West to help it with air power after the loss of Arbil, announced on its radio and television that the Iraqi army was pouring into Kurdistan. Such is the terror of Saddam Hussein's name among Kurds, that, as in 1991, they broke and fled. Mukhtar, a KDP a pesh merga (soldier), who fought at Degala, where the PUK failed to blow up a strategic bridge on the road from Arbil to Sulaimaniyah, said: "They were defeated in their hearts, in their souls. They were throwing away their weapons."
Not everybody is quite convinced that this will last. A foreign observer in Arbil, who has been in the country for the whole of the civil war, said: "Is it likely that the PUK and Talabani, who have succeeded in fighting for many years, will give us just like that?" But most Kurds, soldiers and civilians alike, believe that a come-back by the defeated party will be very difficult. War-weariness is great. Of the chances of renewed warfare with the PUK, Mr Barzani says: "If anything happens it will be because the Iranians are equipping them."
The pesh merga close to the Iranian border agree. At Khasre, a pretty village between mountains, a local KDP leader called Zrar said his forces lost 23 dead failing to hold back the PUK supported by Iranian artillery fire last month. Their position became even more dire when one of their officers, changed sides with 100 men.
Shaking his head in wonderment, Zrar said: "After the fall of Arbil we were able to take our positions driving our cars. Day after day, PUK members are giving up their weapons and surrendering. I don't believe they will be able to send a group over here for a year."
In the vast Kurdish mountains small groups of guerrillas can survive and fight, but to do so requires high morale and resolution. The word pesh marga means literally "those who face death", but the last month has shown that many recruits, paid 1,000 dinars (pounds 22) a month, often six months in arrears, have no intention of getting killed for a warlord on the losing side.
This is not to say that all 3.5 million Kurds, including KDP members, are not deeply shaken by Mr Barzani's alliance, however brief and tactical, with Saddam. But so long as Iraqi troops do not enter Kurdistan and Mr Barzani can provide peace and better living conditions, the majority of Kurds are likely to support him.