Project chairman, Bertrand Piccard, piloted the vehicle from Muscat in Oman to Ahmedabad in India, crossing the Arabian Sea in the process.
Tuesday’s journey took just over 15 hours. The distance covered – 1,468km – set a new world record for a flight in a piloted solar-powered plane.
The vehicle has another 10 legs ahead of it over the course of the next five months.
Included in that itinerary will be demanding stretches when the craft has to fly over the Pacific and Atlantic oceans.
Piccard is sharing the flying duties with project partner and CEO, Andre Borschberg, who made Monday’s inaugural trip from Abu Dhabi to Muscat.
Solar Impulse arrived in Ahmedabad in darkness, its wings illuminated by LEDs, and its propellers driven by the energy stored in its batteries.
The plane had left Muscat at 06.35 (02:35 GMT) and put its wheels down at Sardar Vallabhbhai Patel International Airport at 23.25 local time (17:55 GMT).
Preparations are already under way for the next leg to Varanasi in northeast India, although mission planners say that will not be for another four days, at least.
The time will be spent carrying a campaigning message on the topic of clean technologies to the local Ahmedabad people, and the wider Indian population.
The Solar Impulse project has already set plenty of other world records for solar-powered flight, including making a high-profile transit of the US in 2013.
But the round-the-world venture is altogether more dramatic and daunting, and has required the construction of an even bigger plane than the prototype, Solar Impulse-1.
This new model has a wingspan of 72m, which is wider than a 747 jumbo jet. And yet, it weighs only 2.3 tonnes.
Its light weight will be critical to its success.
So, too, will the performance of the 17,000 solar cells that line the top of the wings, and the energy-dense lithium-ion batteries it will use to sustain night-time flying.
Operating through darkness will be particularly important when the men have to cross the Pacific and the Atlantic.
The slow speed of their prop-driven plane means these legs will take several days and nights of non-stop flying to complete.
Piccard and Borschberg – they take it in turns to fly solo – will have to stay alert for nearly all of the time they are airborne.