Salahuddin Quader Chowdhury and Ali Ahsan Mohammad Mujahid were hanged in Dhaka's central jail.
They were convicted of genocide and rape - charges they denied.
Chowdhury has been an influential politician - he was elected MP six times. Mujahid was a top leader of Bangladesh's largest Islamist party. Home Minister Asaduzzaman Khan said they were hanged after President Abdul Hamid rejected appeals for clemency by the two men.
However, family members have dismissed reports that the men had made any such appeals, which would have also required admissions of guilt.
"My father said he did not seek any mercy," Chowdhury's son, Humam Qauder Chowdhury, told AFP news agency, after meeting his father for the last time hours before his execution. "He has always said he's innocent."
Salahuddin Quader Chowdhury
Better known as Saqa, he was eldest son of the late Muslim League and Chittagong-based leader Fazlul Quader Chowdhury.
His father was the speaker of the National Assembly of undivided Pakistan in 1965 and campaigned for a united Pakistan.
Complained that the tribunal's verdict had come "from the [law] ministry", saying it was on the internet before it was announced in court.
Ali Ahsan Mohammad Mujahid
A student leader in 1971, he supported Bangladesh remaining part of Pakistan
Went into hiding soon after independence, but resurfaced after Gen Ziaur Rahman came to power in a military coup in 1977
Was social welfare minister in the BNP-led government from 2001-2006 and was highly regarded for his organisational skills and oratory
Bangladesh war crimes trial: Key accused
The Supreme Court upheld their sentences earlier this month.
Chowdhury was the most senior leader of the opposition Bangladesh Nationalist Party to be sentenced for crimes against humanity.
Two years ago, a special war crimes tribunal found him guilty of nine out of 23 charges including genocide, arson and persecuting people on religious and political grounds.
The prosecution said that his father's residence in Chittagong was turned into a torture cell during the war.
Mujahid was the secretary-general of Jamaat-e-Islami. He was sentenced to death in July 2013.
He was accused of responsibility for the killings of a number of pro-independence Bangladeshi leaders and intellectuals.
The tribunal found him guilty of five charges, including abduction and murder.
Bangladesh's government says the war crimes trials are necessary to bring murderers to justice.
But the opposition says they have been used to persecute them and human rights groups have said the tribunal does not meet international standards.
