Peshwá, Bájí Rao (1721-40), converted the grant of the tribute of the Deccan, which had been given by the Delhi emperor in 1720, into a Maráthá sovereignty over the Deccan. The second Peshwá also wrested the Province of Málwá from the Mughal Empire (1736), together with the country on the north-west of the Vindhyas, from the Narbadá to the Chambal. In 1739, he captured Bassein from the Portuguese. Málwá was finally ceded by the Delhi Emperor to the Maráthás in 1743.
Third Peshwa, 1740-1761.—The third Peshwá, Balájí Bájí Rio, succeeded in 1740, and carried the Maráthá terror into the heart of the Mughal Empire. The Deccan became merely a starting-point for a vast series of their expeditions to the north and the east. Within the Deccan itself the Peshwá augmented his sovereignty, at the expense of the Muhammadan Nizám of Haidarábád, after two wars. The great centres of the Maráthá
power were now fixed at Poona in Bombay and Nagpur in the Central Provinces. In 1741-42, a general of the Nágpur branch of the Maráthá Confederacy known as the Bhonslas, swept down upon Lower Bengal; but, after plundering to the suburbs of the Muhammadan capital of Murshidábád, he was driven back through Orissa by the Viceroy Alí Vardí Khan. The 'Maráthá Ditch,’ or semi-circular moat around part of Calcutta, records to this day the panic which then spread throughout Lower Bengal. Next year, 1743, the head of the Nagpur branch, Raghují Bhonsla, invaded Lower Bengal in person. From this date, notwithstanding quarrels between the Poona and Nágpur Maráthás over the spoil, the fertile Provinces of the Lower Ganges became a plundering ground of the Bhonslas. In 1751, they obtained a formal grant from the Viceroy Alí Vardí of the chauth, or 'quarter revenue' of Lower Bengal, together with the cession of Orissa. In Northern India, the Poona Maráthás raided as far as the Punjab, and drew down upon them the wrath of Ahmad Sháh Durání, the Afghán, who had already wrested that Province from Delhi. At the battle of Pánípat in 1761, as we have seen, the Maráthás were overthrown by the combined Muhammadan forces of the Afghans and of the northern Provinces which still nominally remained to the Mughal Empire.
