Joshua King put the Cherries in front from the penalty spot after 35 minutes after he had been tripped by Marc Albrighton.
With six minutes of added time played, Mahrez - who almost left the Foxes for Manchester City during the January transfer window - curled in a free-kick to snatch a point.
Foxes boss Claude Puel reflected at full-time: “It would have been better to score before but it was important to get the equaliser because it is a good reward for our mentality today.
“At the end it is not enough. We dropped two more points at home and that is not enough, but it was the minimum to come back in this condition, with all the scenarios.
“It is good momentum because the players believed until the end. I was happy for them because it was tough to keep that strong mentality, to keep going. It was the same feeling from the fans because they pushed their team until the end. It is a shame and a disappointment also because we dropped two points."