Super-sub Abdul Sahal (90') whizzed past the Nepalese defence to nail the final one in the coffin on the last minute of regulation time.
Incidentally, this was Chhetri's fifth goal in as many outings during this campaign to finish at the top of the scoring chart.
India rang in a couple of changes to the starting line-up as Anirudh Thapa and Chinglensana Singh came in for the suspended Subhasish Bose and the injured Brandon Fernandes.
The first chance to the Blue Tigers came in the fourth minute when Yasir played in a delicious ball from the right for Thapa but Nepalese goalkeeper Kiran Limbu came out of his line to grab the ball.
Indian forward line tried every bit to breach the deadlock but the Nepalese defenders kept them at bay in the opening exchanges.
Pritam Kotal curled in a couple of free-kicks at the Nepal 18-yard-box only to see the opposition defenders gain possession of the ball. On the dying embers of the first half, Chhetri came close to scoring his 80th international goal but his volley flew over the crossbar.
As the referee brought an end to the first half, both India seemed to have had the upper hand with more chances created, but could not break the deadlock.
Within four minutes after the resumption, Chhetri made amends for the earlier miss as he headed in a through ball from Kotal to open the scorebook. Chhetri produced a textbook header that was powered into the ground before it bounced in over the line.
Within a minute, Suresh Singh, the former FIFA U-17 World Cupper scored his maiden goal for the Blue Tigers, volleying home a cross by Yasir Mohammad from the right flank.
Thapa and Kotal combined scintillatingly to script another goal in the process but the chance was foiled by Kiran Limbu once again.
With 10 minutes of regulation time left on the clock, Manvir rolled it to second-half substitute Udanta (who replaced Yasir). The winger dispatched it for Chhetri, but defender Rohit Chand made a spectacular interception to avert the danger.
As the Blue Tigers dugout was waiting for the final whistle, Sahal joined the party, as he produced a mazy run around a flurry of defenders, and placed the ball into the back of the net from inside the six-yard box.
Following their record-time eighth SAFF Championship victory, the Blue Tigers will now gear up for the AFC Asian Cup 2021 qualifying third round that is scheduled to kick off next year.