After saving two match points when 5-3 down in the final set, Bartoli evenutally prevailed 7-6 (10/8) 4-6 7-5 in an epic encounter which lasted three hours and 12 minutes.
Bartoli came from 3-5 down in the opening set to take in on a tie-break but only after saving set point in the breaker.
Both players were more consistent in the second set, where there were only three breaks of serve, but Govortsova took it to set up a decider.
It turned out to be a thriller with Bartoli refusing to bend when staring down the barrel.
She actually won the last four games, although getting over the line took some doing.
Bartoli needed five opportunities to seal the victory, while serving for the match, with the final game featuring six deuces and three saved break points.
"It was very difficult to stay alive in that match," said Bartoli afterwards.
"It was a very lengthy, tricky day. I started at 11am and then again at 2pm and we finished at 6pm, so it was a very long match and the rain interruption I think was to my disadvantage because I think I was dominating a little bit initially, physically at least.
"Then I think she was able to recoup during the break with the rain. She was playing really well. She missed pretty much nothing.
"So, if I lost this match, I don't think I would have had many regrets, really, because I did the best I could. I was lucky and I chased down the points when that proved necessary. At the end of the day, I won.''
The French number one recently ended a coaching experiment with former Wimbledon champion Jana Novotna and is now being coached again by her father Walter, but says she has no regrets.
"I've learned a lot out of these recent experiments," she added. "I have no regrets and the situation now is good.
"Whatever happens, I still have a good few years in front of me to produce some good seasons."
Elena Baltacha's Grand Slam return ended in a 6-3 6-0 defeat to New Zealand's Marina Erakovic in the first round of the French Open.
Having waited all day as bad weather disrupted the schedule at Roland Garros, Baltacha's match was finally moved from Court Three to Court Six at 7.45pm local time.
The former British number one is now ranked 200th after taking eight months off following the Olympics to have ankle surgery.
She had expected that to be the end of her career but realised she did have appetite for a lengthy period of rehabilitation after all and played the first tournament of her comeback in America last month.
Since then the 29-year-old has won four matches, including an impressive victory over then-world number 58 Stefanie Voegele in Brussels last week.
Erakovic, meanwhile, has been in terrible form, losing five straight matches before Tuesday's contest, and seven of her last eight.
Baltacha could not have made a better start, breaking her opponent's serve in the first game and holding for a 2-0 lead, but from there her fortunes began to go downhill.
Despite her bad run, which has seen her fall to 92nd in the rankings, Erakovic was hitting big serves and pounding the ball off the ground.
It was proving too much for Baltacha, who saw five successive games go past before holding serve. She then had her opponent at 0-40 serving for the set but could not take any of the chances.
The second set was rather a horror show for Baltacha, who could not find any way of troubling Erakovic, and the New Zealander clinched victory after 56 minutes.
With so much time lost to rain, Heather Watson's match was postponed until Wednesday.
The British number two, who is making her return after more than two months out with glandular fever, will face Swiss Stefanie Voegele.