A match billed as a clash between the two title favourites failed to live up to lofty expectations with both teams struggling to create clear chances at Anfield on Monday (NZDT).
But Mahrez should have won it for City with four minutes to go after Virgil van Dijk was penalised for bringing down Leroy Sane, instead blasting his spot-kick well over the crossbar.
With two unbeaten league records on the line a close match was always likely, City appearing wary of Liverpool's threat having already lost three times to Jurgen Klopp's side in 2018.
And, despite Mahrez's miss, a point apiece was a fair result as both teams cancelled each other out, the draw leaving Liverpool in third, below Chelsea, with all three on 20 points.
Mohamed Salah fired an early shot wide before Dejan Lovren was arguably fortunate not to concede a spot-kick when he bumped Sergio Aguero over in the penalty area.
James Milner had to be replaced due to injury and Liverpool were sloppy thereafter, although City lacked cohesion and the first half ended without a shot on target from either side.
A wild Fernandinho strike from 35 yards that flew well off target summed up City's frustrations, with a low-key Aguero booked for a poor challenge on Jordan Henderson.
Mahrez should have hit the target on the hour-mark, but pulled his effort wide of the post, then Salah shot straight at Ederson as the game finally opened up in the second half.
Alisson denied Mahrez with a smart stop at his near post in the 75th minute, but the best chance of the game was still to come.
Referee Martin Atkinson pointed to the spot when Van Dijk brought down substitute Sane, Mahrez smashing his kick over the crossbar to leave the game deadlocked.