Sawant shot a score of 597 (100,100,100,99,99,99), equalling the 1998 record set by Marina Bobkova of Russia.
The 29-year-old, who clinched gold medals in the Commonwealth Games Air Rifle event, was level with Poland's Ewa Joanna Nowakowska in the final score but managed to clinch the top honours with a better perfect score tally of 41.
Kazakhstan's Olga Dovgun settled for the bronze with a score of 596.
An elated Tejaswini said she only wanted to give her best in the event and was not event thinking about a medal let alone the world record.
"The way we were training, I thought I would be getting my personal best. I was not thinking about a medal or a world record. Having got both, I can't even explain how I am feeling right now. It's just amazing," the shooter from Kolhapur told PTI from Munich.
"My coaches, including Kazakh coach Stanislav Lapidus, made some plans for me and I am glad that everything worked accordingly," she added.
Tejaswini said the although pursuing shooting is no easy task in small towns like hers, she made it big due to her parents' support.
"There are difficulties but instead of complaining, I think it is better to use them as motivation and work harder. That's what my parents taught me while they supported my dreams," she said.
"The more problems you face in pursuit of your dreams, the more delightful your success becomes. As far as problems of ammunition shortage are concerned, at least I have never faced them. My practice has never been held up because of such issues," she added.
Tejaswini said the morale-boosting historic triumph also sets her up perfectly for the Commonwealth Games this October.
"The preparations has been on for a long time and this has just added to my confidence. I can't describe how happy I am right now," she said.
National coach Sunny Thomas was equally elated for his ward.
"She is only the fifth world-record holder in India after Gagan Narang, Suma Shirur, Ronjan Singh Sodhi, Asher Noria. What she did today is truly remarkable," Thomas said.
Asked whether he expected her to achieve the feat, Thomas said more then Prone, he was hoping for a medal from her in the Rifle 3 Position event.
"She was shooting well since yesterday. So I knew she would do something. I was expecting her to win a medal in 3 Position and we were disappointed when she didn't. But she more then made up for it in Prone," he said.
"She is the first woman to do it for India and it is a proud moment for the country," he added.