Unbeaten hosts India defeated New Zealand by 70 runs in Mumbai on Wednesday to make it 10 wins out of 10 this World Cup as they booked a place in Sunday's final in Ahmedabad.
Kohli scored a record 50th one-day international hundred in an imposing total of 397-4 that also featured Shreyas Iyer's rapid 105 off 70 balls before Mohammed Shami cleaned up with a stunning seven-wicket haul.
But it was opener Rohit, on his Wankhede Stadium home ground, who set the tone with a 29-ball 47 after winning the toss.
Hussain said Rohit, appointed India's white-ball captain in December 2021, deserved plenty of credit for India's run to the final.
"The headlines will be about Kohli, about Shreyas, about Shami. But the genuine hero of this Indian side, the man who has changed the culture, is Rohit Sharma," Hussain told Sky Sports.
The former England captain, himself born in Madras (now Chennai), added: "It's one thing coming in the group stage, but can you do it again, can you play fearless cricket in a semi-final?
"Their skipper went out there and showed everyone, showed his dressing room that they're going to carry on in exactly the same way."
Kohli may be the tournament's leading batsman with 711 runs, but Michael Atherton - another ex-England captain - said the manner in which Rohit, who has now scored 550 in this World Cup himself, batted on Wednesday was telling.
'Sending a message'
"For a team who have occasionally blinked when the critical moment has arrived in recent ICC events, often tip-toeing through an innings, Rohit led brilliantly, as he has throughout a campaign where he has eschewed personal milestones and batted selflessly against the new ball," Atherton wrote in The Times.
"It was not the number of runs that he scored, but the message he sent in getting India off to a flyer, making 47 in only 29 balls, that was vital. Don't go into your shells, he was saying."
Yet in a match where 724 runs in all were scored, despite concerns about a used pitch, it was paceman Shami who had the final say with an extraordinary return of 7-57 - the best by any bowler in a World Cup semi-final.
Shami was out of the India team for the first four matches of the tournament and might not have featured at all but for an injury to Hardik Pandya.
Yet heading into Thursday's second semi-final between Australia and South Africa, he was the leading bowler at the World Cup with 23 wickets from six games at the astonishingly low average of under 10 apiece.
England's 2019 World Cup-winning captain Eoin Morgan, who faced Shami during his career, said: "The level of control he has shown throughout this tournament to move the ball off the seam and in the air has been great to admire.
"Seven for 57 in a one-day international is unheard of, particularly in a World Cup knock-out game where there is a huge amount of pressure on him... to have someone like that at your disposal for Rohit Sharma adds more value to the strength of India."
