Aliyev, who died of heart failure on Friday, dominated Azerbaijan politics for three decades. He was 80 years old.
His son, Ilham, dubiously elected president in October, headed a procession on Monday along streets lined with red carnations.
The coffin, draped in the green, red and blue flag of the Caspian Sea state, was borne on the two-hour journey by a gun carriage. Thousands of people had earlier filed past the coffin as it lay in a concert hall.
"Who will take care of us now?" said Fatakh Usifzade, 56, as he passed into the cemetery, where Aliyev was laid next to his wife Zarifa in the Avenue of Honour. "Azerbaijan will never again have such a president."
Soldiers and police eased the passage of mourners into the cemetery, clearly too small to hold them all.
Haider Aliyev was condemned for
human rights abuses
Five cannon shots sounded over the grave and long lines of distraught Azeris filed into the grounds late into the evening.
Ilham had earlier greeted mourners in the concert hall, where the coffin of his father lay.
Russian President Vladimir Putin was the most high-profile foreign dignitary at the funeral.
But heading the US delegation was Elizabeth Jones, the Assistant Secretary of State for European and Eurasian Affairs - reflecting Washington's good relations with the country.
"Azerbaijan was lucky that he was the head of this state... I am sure that the memory of him will not only be preserved in Azerbaijan but also in the whole post-Soviet area," Putin said.
Ilham Aliyev was accused of
stealing the presidential election
The only regional leader not in attendance was President Robert Kocharyan of Armenia. The two states remain locked in a dispute over the territory of Nagorno-Karabakh, where a truce was declared in 1994 after six years of war left 35,000 dead.
Aliyev, who led the Azerbaijan through nearly all of its period of independence, handed power to his son earlier this year.
He is widely credited with successfully expoliting his country's oil wealth and creating social stabilty.
But his detractors said he had scant regard for human rights and ruled his country with an iron fist.
They have also accused his son of effectively stealing last October's presidential elections, which were widely condemned by international observers.
Analysts have raised question marks over Ilham Aliyev's long-term prospects and suggested he lacks his father's mettle.
But Aliyev junior has in effect been running the country for several months and, however inexperienced, analysts say he is safe for now.