It took a stoppage-time goal from Goncalo Ramos to force the draw.
A win would have given overwhelming favourites PSG a third straight French title, and a record-extending 12th overall.
The capital club extended their lead to 12 points over second-placed Monaco, who have four games left: PSG can still become champions this weekend if Monaco drop points against Lyon on Sunday (Monday AEST).
"Even though mathematically it's not done yet, I think we can say tonight that we are the champions," PSG coach Luis Enrique told broadcaster Canal Plus.
Perhaps mindful of his side's Champions League semi-final against Borussia Dortmund on Wednesday, Enrique rotated his team, starting superstar forward Kylian Mbappe on the bench.
Le Havre scored against the run of play in the 19th minute when winger Emmanuel Sabbi fed Christopher Operi, who buried an angled shot into the far corner.
Bradley Barcola equalised, converting a low cross from Warren Zaire-Emery in the 29th minute, but instead of being discouraged Le Havre raised their level and Andre Ayew made it 2-1 with a deflected shot shortly before halftime.
Enrique tried to shake things up by sending on Mbappe, Lee Kang-in and Senny Mayulu for Barcola, Ousmane Dembele and Marco Asensio at the break.
But Le Havre were unfazed and added a third goal from a penalty by Abdoulaye Toure on the hour mark, after Danilo fouled Loic Nego.
Enrique used up all his substitutions moments later, replacing Marquinhos and Randal Kolo Muani with Milan Skriniar and Ramos.
Ramos brought more desire on the field, feeding Achraf Hakimi, who pulled one back by beating goalkeeper Arthur Desmas in the 78th minute.
The Portugal international salvaged a point in the fifth minute of stoppage time by heading a cross from Lee into the bottom corner.
"You must stay focused for the full 90 minutes against the big teams. We didn't manage to do that, unfortunately," Le Havre goalscorer Operi said.
"But we can be proud of our performance and of that point earned because that point will count for us at the end of the season."
The draw moved Le Havre out of the relegation play-off spot.
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