Before a crowd of onlookers in Mumbai's Oval Maidan recreation ground, Kate bravely wielded a cricket bat as the former Indian captain, one of the game's greats, bowled a delivery to her.
Prince William also took his turn at the batting crease, demonstrating his prowess at the sport, which is hugely popular in India, as the royal couple participated in a number of sporting activities with local children.
Earlier, the couple began their first visit to India by laying a wreath for the victims of the Mumbai terror attacks
at the Taj Mahal Palace Hotel, where dozens of people were killed during a three-day siege by Islamist terrorists in November 2008.
They also met with hotel staff who helped protect guests during the attacks, Kensington Palace said on its Twitter feed.
After the sporting session in the park, the couple visited the city's ancient Banganga water tank, where they were greeted with dancers, and presented with garlands to scatter on the water.
In the evening, William and Kate were scheduled to attend a Bollywood gala, to raise funds for charities they had met during during the day.
On their arrival in Mumbai, the royal couple were informed of the deadly temple fire in Kollam, where scores of people perished Sunday.
The Duke and Duchess were "saddened by the news and send their thoughts to all who are assisting the victims," a spokesman for Kensington Palace said.
The next legs of the tour will see them visit India's capital, New Delhi, Kaziranga National Park in the state of Assam, the Himalayan kingdom of Bhutan, and Agra, home of the Taj Mahal.
The tour follows criticism of Prince William in Britain's tabloid press in recent months over perceptions he was slacking off from his responsibilities as a senior royal.
Last month, his younger brother, Prince Harry, made a five-day visit
to the neighboring Himalayan nation of Nepal.