India defeated Australia by eight wickets to level the four-match Test series 1-1.
Chasing 70 for a win, it was only poetic justice that Rahane hit the winning run of Nathan Lyon as India made a thrilling comeback in the series. The win also ensures India moves a step closer to the final of the World Test Championship.
Kohli said it was an amazing effort by Team India and hailed Rahane for his captaincy.
"What a win this is, absolutely amazing effort by the whole team. Couldn't be happier for the boys and specially Jinks who led the team to victory amazingly. Onwards and upwards from here," Kohli tweeted.
Riding on the back of the confidence from day three, India first dismissed Australia for 200 and then came back to chase the target of 70 in just 15.5 overs.
If one session had cost India the first Test, it was again a session -- which Rahane and Ravindra Jadeja weathered on day two - that saw India bag the second game.
However, the win wasn't as easy as it shows on paper. Pat Cummins and Mitchell Starc gave Australia the early wickets to ensure the win won't be a cakewalk for the visitors.
Starc dismissed Mayank while Cummins sent Pujara back as a small target started looking a little bigger. However, some assured strokeplay from Gill and Rahane calmed the nerves of India's dressing room.