The attacks outside Makhachkala late on Thursday were the deadliest in months, undermining efforts by Russian security forces to contain an Islamist insurgency in the North Caucasus near Sochi, where Russia will host the Winter Olympics in 2014.
More than a decade after federal troops toppled an Islamist government in Chechnya, also in the North Caucasus, security forces are fighting militants whose ranks are swollen by anger at poverty, clan feuds and pervasive corruption.
The first suicide bomber detonated a bomb when police stopped a vehicle to check documents, a statement by the National Anti-Terrorist Committee said.
The second explosion came when fire brigades and ambulances arrived, causing additional casualties.
A witness at the scene said a fire truck was reduced to charred wreckage.
"After the blast, only the wheels of the truck remained whole," the witness told reporters.
Local officials said that in addition to the 12 killed in the blast, 90 had been taken to hospital and 20 were treated at the scene.
"Fragments of human bodies are scattered at the post," Russia's Interfax news agency quoted a law enforcement official as saying.
Local investigators said they had found the remains of a man and a woman suspected of being the suicide bombers.
Thursday's blasts were heard by residents far away in the centre of the provincial capital of Makhachkala.
The attacks fell just three days before Vladimir Putin, who sent troops 12 years ago to crush rebellion in Chechnya, is to be sworn in as president.
The unofficial Islamist website www.kavkazcenter.com said the police post was almost completely destroyed. A nearby gas pipeline also was damaged during the attack, RIA news agency reported.
Dagestan faces near daily shootings and bombings blamed on Islamist rebels. It has become the epicentre of violence in the low-level insurgency across the mainly Muslim North Caucasus following two separatist wars in Chechnya.
The insurgents want to create an Islamic state in the region and say they were behind a suicide bombing at Moscow's Domodedovo airport that killed 37 people in January 2011 and twin bombings that killed 40 people on Moscow's metro in 2010.
Russian leaders had expressed concern that the rebels would try to stage attacks in big Russian cities to mar the parliamentary election last December and the presidential elections in March, but no such attacks were reported.