The Kerala-based Grandmaster remained unbeaten in the nine-round tournament.
The 18-year-old Indian lost 0.5-1.5 in tie-breaks in rapid games to the World No. 1.
On Thursday, two tie-breakers will be played to decide the champion.
In the middle of a major time crunch, Praggnanandhaa was able to hold Carlsen for a draw in an objectively equal position with white pieces. The Indian played a solid game and agreed to a draw on move 35.
The Indian Grandmaster, hailing from Tamil Nadu, stunned World No. 2 Fabiano Caruana in the semifinals.
Gujrathi won the match with black pieces as he exploited a tactical oversight from his famous opponent.
The lawsuit, filed at a US District Court in Missouri, also lists Carlsen's online chess platform Play Magnus, Chess.com executive Danny Rensch and American Grandmaster Hikaru Nakamura as defendants.
Carlsen, 31, withdrew from the Sinquefield Cup in St Louis, Missouri, earlier this month after losing to the 19-year-old, who lags him by almost 200 Elo points.
The international chess body also rebuked the world champion for abruptly resigning an online game recently.
Carlsen finished with 16 points to the Indian prodigy's tally of 15.