To be brief, it didn't. After the breakup of the British East India Company in 1858, the British monarchy 'ruled' India (i.e. Victoria was Empress of India, with a viceroy to rule in her stead in India), however there were a number of governors, princes and magistrates beneath the viceroy that were responsible for the day-to-day management of their respective province. The viceroy's power was comparable to the Queen's power in Britain – influential on policy, but with little direct authority.

Now, the bigger question here is, of course, why create a viceroy at all? This is a more complex question, but the simple answer is two-fold: convenience and ideology.

Regarding convenience, British authority (and territory) waxed as Mughal authority waned, thus the BEIC took on the broad, pan-Indian territorial responsibilities of the previous empire. Such an action was not unprecedented; in fact, the Mughals themselves had followed a similar path in their own ascendancy versus the Delhi Sultanate in the 16th-17th centuries.

Regarding ideology, there was a common assumption amongst British statesmen (particularly those involved directly in Indian affairs) that Indian 'oriental' sensibilities required a form of authoritative, despotic leadership in order to maintain law and order and, ultimately, to check what would otherwise become uncontrollable barbarism. This was a highly Eurocentric and, for the lack of a better term, orientalist view, though many Britons were keen to point out that India need not be ruled despotically forever. Many Britons believed that an India governed by Britain (even a despotic Britain) would eventually follow the same historical narrative of 'barbaric Britain' under Rome, in that imperial authority would catalyze the emergence of sensible and 'modern' Indian values. This ideology would have profound implications for future Anglo-Indian relations, however that is another issue entirely.

To bring my answer back to your original question, Britain's rationalization regarding despotism, plus the imperial reality of Mughal India, made a 'centralized' Indian government the most logical, efficient, and financially prudent method of rule, on that carried over into the Raj after 1858.

Sources:

Thomas Metcalf, "Ideologies of the Raj"

David Cannadine, "Ornamentalism"

C.A. Bayly, "Imperial Meridian"

The British did not treat India as one entity from the start. When they entered India at the beginning of the 17th century, it was under the guise of peaceful trade relations. They did, however, heavily fortify their "trading outposts" essentially making them bunkers. At the time, there were several warring factions in India, including the Mughals lead by Jehangir, the Marathas lead by Shivaji and several French, Dutch and Portuguese dominions.

Over a period of 150 years, the British outgunned, outpaced, outmaneuvered and, eventually, outlived all of these competitors. The concept of "India" at the time was more cultural than geographical. Starting in the east, the British began to usurp territory one King at a time, conquering Bengal and Bihar at the Battle of Plassey in 1757. Robert Clive, the Hero of the seven year war, was instrumental in this crusade.

The policy they employed has become a legend in Indian history textbooks, today referred to as "divide and conquer". Through subterfuge and tactical friendships, the British gained a firm foothold in India and cobbled together a "country", similar in shape and size to the geopolitical landmass we refer to today as the Indian subcontinent.

The East India Company was formally dissolved in 1857 and all its properties were ceded to the Queen. After another 90 years of Crown rule, during which the British had further reshaped and mutilated "India", independence was granted and, at the stroke of the midnight hour on August 15th, 1947, independence was granted, to India and Pakistan both.

TL;DR: The British didn't treat it as one entity to begin with, but eventually it became easier to administer it as one colony. Rightly so, imo.