Most Indians don’t know that the Russians actually sent a nuclear warship and two groups of nuclear submarines fitted with an array of ready to fire nuclear warheads, cruisers and destroyers to counter the U.S’s seventh fleet and a British warship during the 1971 war with Pakistan.
Before 1971 the state of Bangladesh never actually existed, it was called East Pakistan and was under the control of West Pakistan(Known as just pakistan today). To counter the rising political influence of Bengalis in East Pakistan the Pakistan army feared losing control and started killing Bengalis by thousands in the eastern front. This created a potential problem for India as lakhs of refugees wanted to come to India for shelter and food. It was then that India took upon herself the onerous task of liberating East Pakistan from Pakistan’s clutches. Alarmed at this threat the Pakistanis soon went to their most important ally(A nation which supposedly calls itself the champion of human rights and democracy).
The Soviet Union sympathised with the Bangladeshis, and supported the Indian Army and Mukti Bahini during the war, recognising that the independence of Bangladesh would weaken the position of its rivals—the United States and China. The USSR gave assurances to India that if a confrontation with the United States or China developed, it would take counter-measures. This assurance was enshrined in thesigned in August 1971.
The United States supported Pakistan both politically and materially. President Richard Nixon and his Secretary of State Henry Kissinger feared Soviet expansion into South and Southeast Asia. Pakistan was a close ally of the People’s Republic of China, with whom Nixon had been negotiating aand where he intended to visit in February 1972. Nixon feared that an Indian invasion of West Pakistan would mean total Soviet domination of the region, and that it would seriously undermine the global position of the United States and the regional position of America’s new tacit ally, China. Nixon encouraged countries like Jordan and Iran to send military supplies to Pakistan while also encouraging China to increase its arms supplies to Pakistan.
The Nixon administration also ignored reports it received of the “genocidal” activities of the Pakistani Army in East Pakistan, most notably the. This prompted widespread criticism and condemnation both by the United States Congress and in the international press.
Then-US ambassador to the United Nations George H.W. Bush—later 41st President of the United States—introduced a resolution in the UN Security Council calling for a cease-fire and the withdrawal of armed forces by India and Pakistan. It was vetoed by the Soviet Union. The following days witnessed a great pressure on the Soviets from the Nixon-Kissinger duo to get India to withdraw, but to no avail.
It has been documented that President Nixon requested Iran and Jordan to send their F-86, F-104 and F-5 fighter jets in aid of Pakistan.
When Pakistan’s defeat in the eastern sector seemed certain, Nixon deployed Task Force 74 led by the aircraft carrierinto the Bay of Bengal. The Enterprise and its escort ships arrived on station on 11 December 1971. According to a Russian documentary, the United Kingdom deployed a carrier battle group led by the aircraft carrier HMS Eagle to the Bay of Bengal
It was then that India activated a secret pact of the Indo-Soviet union agreement, that the soviet union would unconditionally protect its allies from any harm.
On 6 and 13 December, the Soviet Navy dispatched two groups of cruisers and destroyers and a submarine armed with nuclear missiles from Vladivostok; they trailed US Task Force 74 into the Indian Ocean from 18 December 1971 until 7 January 1972. The Soviets also had a nuclear submarine to help ward off the threat posed by USS Enterprise task force in the Indian Ocean.
The British were shit scared by the Soviet aggression and even before entering the Arabian sea they diverted their warship towards the southern Mediterranean. The U.S.S Enterprise even though the largest warship in the world knew that it was literally surrounded by Soviet nuclear submarines and had to retreat. They couldn’t possibly risk a war with Soviets.( Remember the U.S.S.R was a superpower back then).
What is also less known is that the Soviets warned the Chinese that any provocation from their side in this issue would be dealt with appropriately.
This was one of the fundamental reasons why India was always a Pro-Russian country and always will be. Today, 68 years after independence India is not like what she was 4 decades ago, she can successfully defend herself against most naval and air threats.
However one shouldn’t get overly sentimental as Russians are no saints either, the reasons as to why they supported India to such an extent are unclear given the range of brutalities their army was capable of(esp during WWII and the Afghan war).
EDIT: Some people here may brand this answer a propaganda, its seriously not. Please do go through the sources.