The hosts also face Argentina, Tonga and an African qualifier while the Romanians go into Pool D alongside France, Ireland, Italy and Canada.
Both teams went into the game in Tbilisi, attended by a capacity crowd of 27,000, already safe in the knowledge their participation at the 2015 Rugby World Cup in England was guaranteed.
Georgia led 16-9 at half-time thanks to a try by Davit Zirakashvili, with all other points coming from the boot of full-back Merab Kvirikashvili, and now go into their fourth consecutive World Cup, having notched up two wins in twelve matches.
Russia finished third in the European Nations Cup and will have a chance of making the World Cup through play-offs, with five places still to play for.
The African qualifier will be known by July 5 after a tournament between Zimbabwe, Madagascar, Kenya and Namibia.
Meanwhile, Uruguay and the United States play home-and-away fixtures on March 22 and 29 for the American qualifying spot while in Asia, Japan are favourites to win the April 26-May 25 Asian Five Nations as top qualifier and in Oceania, Fiji play the Cook Islands on June 28.
Two play-offs will then be contested for the last remaining place at a date to be decided.