The spectacular attack in Jalalabad, the capital of the eastern Nangarhar province, was the latest in the countdown to next month's presidential elections.
The assault involved a suicide bomber, two remotely detonated bombs and seven insurgents and set off a four-hour gunbattle with the police.
By the time it was over, all seven insurgents involved in the multi-pronged attack were killed, said Deputy Interior Minister Gen Mohammed Ayub Solangi.
The attack began with a suicide bomber detonating his explosives-laden car outside the police station, located near the palatial residence of the province's Governor Attahullah Ludin.
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Solangi said the insurgents were armed with heavy weapons and automatic machine guns. The battle was fierce with the Afghan troops fighting their way out and chasing the attackers down the street and when it ended, 10 policemen, including a district police chief, were dead.
The one civilian who was killed was a university student caught in the cross-fire, said police.
Doctors at nearby hospitals said as many as 20 civilians were wounded, mostly from shrapnel from the initial suicide car bombing, but that the majority were treated and released quickly. Two of the wounded were said to be in serious condition.
In an email in Pashto the language most often spoken by the Taliban the insurgent group's spokesman Zabihullah Mujahid said the Taliban had staged the attack in Jalalabad.
The Taliban have carried out numerous attacks in Jalalabad and the country's east, which is their traditional stronghold, along with southern Afghanistan.
They have threatened a campaign of violence to disrupt the April 5 vote, which will choose a new Afghan president to lead the country as foreign troops prepare to end their combat mission by the end of the year.