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 - 1,468 km - set a new world record for a 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 ofclean technologies to the local Ahmedabad people, and the wider Indian population.
Solar Impulse heads out over the Arabian Sea
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.
They will be permitted only catnaps of up to 20 mins - in the same way asingle-handed, round-the-world yachtsman would catch small periods of sleep.
They will also have to endure the physical discomfort of being confined in a cockpit that measures just 3.8 cubic metres in volume - not a lot bigger than a public telephone box.
Bertrand Piccard looking fresh after more than 15 hours in the cockpit of Solar ImpulseThe Solar Impulse venture recalls other great circumnavigation feats inaviation - albeit fuelled ones.
In 1986, the Voyager aircraft became the first to fly around the world without stopping or refuelling.
Piloted by Dick Rutan and Jeana Yeager, the propeller-driven vehicle took nine days to complete its journey.
Then, in 2005, this time was beaten by the Virgin Atlantic GlobalFlyer, which was solo-piloted by Steve Fossett.
A jet-powered plane, GlobalFlyer completed its non-stop circumnavigation in just under three days.
Five-day solo flight over the Pacific - Solar Impulse's biggest challenge?
Pilot Andre Borschberg gives a guided tour of the solar plane
Andre Borschberg is a trained engineer and former air-force pilot, he has built a career as an entrepreneur in internet technologies.
Bertrand Piccard is well known for his ballooning exploits. Along with Brian Jones, he completed the first non-stop, circumnavigation of the world in 1999, using the Breitling Orbiter 3 balloon. The Piccard name has become synonymous with pushing boundaries.
Bertrand's father, Jacques Piccard, was the first to reach the deepest place in the ocean (a feat achieved with Don Walsh in the Trieste bathyscaphe in 1960). And his grandfather, Auguste Piccard, was the first person to take a balloon into the stratosphere, in 1931.
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