The "real time" list of the richest Indians on the business magazine's website showed Shanghvi with a net worth of $22 billion, and Ambani, who chairs the giant Reliance Industries group, behind with $20.4 billion.
The switch comes just three days after the Forbes list for 2015 confirmed 57-year-old Ambani as India's top billionaire for the eighth straight year.
But a surge in the shares of Shanghvi's Sun Pharmaceutical Industries on Wednesday helped his wealth count rise to the top spot on Forbes' real time tracker.
Shanghvi's business profile has rocketed after he bought out troubled pharma peer Ranbaxy Laboratories last year from Japanese giant Daiichi Sankyo for $3.2 billion.
The buyout surprised Indian markets but the acquisition has been caught in a legal tangle and is yet to be completed.
The fortunes of Reliance Industries and Mukesh Ambani, who lives in a 27-floor home worth at least a billion dollars in Mumbai, have been hit as falling global crude prices dented the firm's major revenue sources from petrochemicals and refining.
In global rankings of wealth, 59-year-old Shanghvi is now in 37th place while Ambani is 42nd, Forbes data showed.
The three other Indians in the top 100 global list are Azim Premji, owner of IT major Wipro, in 47th, followed by HCL Technologies' founder Shiv Nadar at 63rd and steel magnate Lakshmi Mittal at 84th.
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