The English East India Company's tenth voyage was a gamble funded by subscription stock. Best's flagship Red Dragon, accompanied by the Hosiander, James, and Solomon, set out from Gravesend on 1 February 1612, sailing via Trinidad and then along the Indian coast past Daman before reaching Surat on 5 September. Surat was the principal port of the Mughal Empire, sitting at the mouth of the river Tapti, and the Portuguese had monopolized European trade with India since the late 15th century. When a squadron of 16 Portuguese barks sailed into Surat on 13 September, the stage was set for confrontation. Best found himself navigating simultaneously between two powers: the Portuguese, who intended to keep their monopoly, and the Mughal governor, whose cooperation he needed for trading rights.

The weeks before battle were a tangle of diplomacy and coercion. Best sent an emissary to the Mughal Emperor requesting permission to trade and establish a factory at Surat. Meanwhile, two of his men, the purser Canning and William Chambers, were arrested on shore. Best responded with the directness that would define English commercial practice in India for centuries: he detained a ship belonging to the Governor of Gujarat and offered a prisoner exchange. By early October, Best had sailed to Suvali, about 12 miles north of Surat, where the governor was occupied battling a Rajput rebellion. Between 17 and 21 November, amidst this chaos of competing interests, Best managed to negotiate a treaty granting trading privileges, subject to the Emperor's ratification. The Portuguese, watching their monopoly threatened by ink on paper, decided to settle the matter with cannon.

A skirmish on 29 November produced little damage on either side. The real engagement came at daylight on 30 November. Best sailed Red Dragon directly through the line of four Portuguese galleons commanded by Captain Major Nuno da Cunha, a maneuver bold enough to ground three of the enemy ships. Hosiander closed from the opposite side. The Portuguese managed to refloat their galleons, but the initiative had shifted decisively. That night, the Portuguese sent a bark loaded with combustibles toward the English ships as a fire ship, an old Mediterranean tactic designed to burn an anchored fleet. The English watch spotted it in time, and cannon fire sank the bark, killing eight men aboard. A standoff held until 5 December, when Best sailed for the port of Diu, his point made.

On 6 January 1613, Best received the Emperor Jahangir's letter ratifying the trading treaty. The Mughal governor's report of the battle had reached the emperor, and the English defeat of Portuguese naval power impressed him enough to favor the newcomers over the established colonial presence. Best dispatched Anthony Starkey overland to England carrying news of the success. Starkey never arrived; the English claimed he was poisoned by Jesuit priests along the route. Best continued to Ceylon and Sumatra before returning to England in April 1614. The battle convinced the East India Company to establish a small naval force to protect its commercial interests, a modest beginning that is regarded as the origin of the modern Indian Navy. Swally itself became the Company's first protected port on the Indian coast, chosen because its waters offered shelter from both sudden squalls and military assault.