Andrew Conway scored a late try but Munster could only salvage a draw from a thrilling Thomond Park clash.
Reds head coach Johann Van Graan acknowledged the result could have gone either way.
Racing looked well placed to become only the second French club in 32 attempts to win a Champions Cup match in Limerick when leading 21-14 inside the final 10 minutes.
However, the late try from winger Conway, superbly converted from the touchline by fly-half JJ Hanrahan, ensured the tie.
Hanrahan, who kicked 11 points in all, even had the chance to sneak an unlikely victory for the hosts at the death but his drop-goal attempt flew left and wide.
The impressive French side scored three converted tries through talismanic No.10 Finn Russell, Teddy Thomas and Juan Imhoff, only for Munster – whose lone try was run in by Keith Earls close to half-time – to fight back.
South African Van Graan said: “It was a very tough game of rugby, two heavyweight boxers who went at each other until literally the last second of the game.
“I thought Racing started pretty well, we came back, we had that chance when we were five metres short about 10 minutes before
half-time. We scored on the stroke of half-time and I thought we played some very good rugby in the first half.
“There was a big breakdown battle, we fell behind in the second half, came back and I thought our bench made a big impact and we got ourselves back to 21-21 with that try and a brilliant conversion from JJ from the sideline.
“We fought back with an incredible kick from Earlsy to get that lineout and then to keep punching in a drop-goal position and unfortunately it went to the left. If that goes over, it’s a different ball game.
“All credit to Racing as well, I thought both teams came to play some very positive rugby. It is like last year’s draw in round one against Exeter – you could have lost it and you could have won it right there at the death. We will take our points and move on.”
The result marked the third year in a row that Munster have recorded a win and a draw in their opening two pool fixtures.
Both sides had to be satisfied with taking two points from the heavyweight clash before the back-to-back phase of Pool Four, with Munster locking horns with holders Saracens next month.
The game was Simon Zebo’s first outing against his native Munster since his move to Racing in summer 2018. Playing at full-back against his former team, the Corkman enjoyed the occasion and felt a draw was the right result.
Having been warmly received by the home crowd, Zebo told BT Sport: “The reception was incredible, as always. The Munster fans are up there with the best in the world. To come back here and play in the Racing colours, I was very proud.
“It was a very close game so probably a deserved draw. We were a bit sloppy at times. It’s a very difficult place to come and be within such a grasp of winning the game so we did ourselves proud.
“It was a huge result for us. The other teams in the group will find it difficult to come away from here with anything.”
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