The 1971, two-week war following the Pakistan Civil War is viewed as the war that had the most profound impact on both countries. Indeed, the 1971 war was sparked by the 1970 Civil War in Pakistan. The civil war was elicited when Zulkifar Ali Bhutto refused to give up his premiership when the Awami League won the elections, resulting in mass riots and arrests of dissidents. President Yahya Khan then called in the military, exiling the Awami League and capturing their leader. In April 1971, exiled Awami League members formed a new government in East Pakistan and declared it to be Bangladesh, an independent state. Guerilla forces, civilian forces and even defected elite forces from West Pakistan came together to form the Bangladesh Army, and thus started to struggle against Pakistan for independence.
It was through this civil war that Indo-Pakistan relationships deteriorated as India provided refuge and help for the Bangladesh troops. Indian Prime Minster Indira Ghandi then launched a diplomatic offensive against Pakistan by signing a peace and cooperation treaty with the Soviet Union, greatly shocking the US and ensuring that the PRC, an ally of Pakistan, would not intervene in the upcoming war. On 3 December 1971, Pakistan suddenly launched an aerial attack on Indian bases, causing India to retaliate and routing the Pakistani army. After only just a fortnight, Pakistan surrendered. The war resulted in Bangladesh gaining independence from Pakistan, and Zulfikar Ali Bhutto assuming presidency of a now much smaller Pakistan after Yahya Khan resigned.
This war can also be said to be an indirect proxy war of the Cold War as US supported Pakistan forces politically and economically, sending supplies to Pakistan in support of their army. The USSR, on the other hand, backed the Indian army after signing the Indo-Soviet friendship treaty.
This was the war that defined India and Pakistan as we know them today. The liberation of Bangladesh from Pakistan created the world's third-most populous Muslim nation. India had also asserted its status as an ally of Soviet Union, a partnership that would last until the dissolution of the USSR. India's declaration to be an ally of Soviet not only generated shockwaves across the White House; it also prevented China from interfering, further highlighting the bipolar situation of the world during that time. The politics involved in the Cold War was again witnessed in this war as US, China and the USSR played their own game during the war.
The Indo-Pakistani War of 1971 was indeed the largest-scaled war between the two countries. Cultural differences arising due to conflicting religious belief had obviously played a huge role in eliciting the third war in as many decades. Upon further scrutiny, this war was actually an exacerbation of the tensions that had arisen through the first two wars. The cultural factors involved are also similar as the war was in fact caused mainly by India's interference in Pakistan's civil war.