On by far the sunniest, warmest day of the tournament to date, Murray lost his range, was beaten by numerous drop shots and at times, was nearly unable to even keep the ball in play at times.
"I showed a lot of heart the last few days in tough, tough matches, a tough atmosphere (against Bourgue)", he said.
One small consolation: Defending champion Stan Wawrinka isn't firing on all cylinders, either. Karlovic could easily win a set but betting on that seems way too risky.
"There won't be many sets in the year where that's the case, so it's fairly rare", said the Scot. "Today there were many ups and downs, but I have my tennis and I'm ready to step it up".
On Wednesday he had no trouble with Andrey Kuznetsov, eliminating the Russian in a very comfortable three-set match 6-3, 6-3, 6-3.
According to the ATP Performance Zone stats, the Briton has won 85 percent of his matches on clay since 2015, more than any other player, including Serbian winning machine Novak Djokovic.
"At the end of the third set, I just thought what happened?".
"Then when I got the break, and then again, I all of a sudden was able to relax and sort of play with the crowd".
Sania Mirza, Leander Paes, and Rohan Bopanna got their French Open campaigns off to a winning start as they won their respective doubles matches to enter the second round.
Men's eighth seed Milos Raonic also made hay in the sun against a French player, crushing Adrian Mannarino 6-1 7-6(0) 6-1, his reward a third-round against lucky loser Andrej Martin.
Bourgue wasted the first of his three break points but forced an error to take the second as his opponent fired a forehand into the net. And he also credited his hugely impressive opponent.
Like Murray, third seed Wawrinka suffered the first-round fright in a five-setter against Lukas Rosol.
Jimmy Connors reached the third round at the French and US Opens in 1991, aged 38. She launched quickly into interviewer mode.
With third-ranked Angelique Kerber and fifth-ranked Victoria Azarenka both falling in the first round, Garbine Muguruza has a path through the women's draw. "I was 6-2, 2-0 ahead. But for the second straight day, it was the Scot who emerged victorious in a five-set tussle that captivated those assembled on the main Philippe Chatrier court".
"I couldn't believe it myself", Bourgue said. "It's not the same thing in women's singles at all".
"It's the only time when being old is OK", Karlovic said.
The Scotsman saw out the set and finally looked to be in control as he broke twice more in the deciding set to move to within one game of a gruelling victory.
Murray could only manage 12 points in the second set.
Instead, from 6-2 2-0 up, he lost 24 of the next 27 points and eight games in row, and then found himself two sets to one down.
Garcia did not surrender without a fight, saving one more match point before bowing out.
Romania's Halep, runner-up to Maria Sharapova in 2014, took a while to tame Kazakhstan's Zarina Diyas to win 7-6(5) 6-2. The trainer taped up her foot and ankle.
If he was never as close to defeat as he was to Stepanek, when the Czech was two points from knocking him out on two occasions in the final set, it was the way his game crumbled in the middle of the match that will perhaps be of the biggest concern.