Premier League: Hull 0 Leicester 1
Mahrez collected a pass 20 yards from goal just after the half-hour at the KC Stadium and netted his second league goal of the season past Allan McGregor.
Hull had started well but wasted the few openings they were able to create, and Mahrez punished them in a scrappy first half.
Steve Bruce made three attacking changes in the second half to try and get his side back into the game, however they were unable to turn possession into goals despite Paul Konchesky's late red card.
Leicester, who were twice saved by the post, absorbed all Hull could throw at them pressure, with Stephen Quinn also given his marching orders for handball in stoppage time as Nigel Pearson picked up a first win at his former club since leaving them in 2011.
Victory is bottom club's Leicester's first since September's memorable 5-3 win over Manchester United – a run of 13 games – and moves them to within three points of safety, with Hull one of three sides firmly in their sights as pressure grows on Bruce.
Jake Livermore returned for the suspended James Chester in Hull's only change from Boxing Day's win at Sunderland, while Leicester rotated their central midfield pairing with Esteban Cambiasso and Matty James coming in.
Sone Aluko, who was again deployed as a lone striker, caused trouble for the Leicester defence in the opening exchanges with his pace, and had the game's first chance after six minutes, but his curling effort from 20 yards was easily saved by Ben Hamer.
Further chances fell to Robbie Brady and Gaston Ramirez in the opening 20 minutes, but neither player was able to stretch Hamer.
Having started well, Hull were made to pay for their wastefulness as Mahrez fired Leicester in front after 32 minutes.
The Algerian collected a pass from David Nugent on the right, cut inside and – having beaten two Hull challenges – fired into the bottom corner from the edge of the penalty area.
Ahmed Elmohamady should have sent Hull into the break level in first-half stoppage time as he met a pinpoint cross from Quinn, but the right-back miscued his volley wide.
Hull introduced Nikica Jelavic, Abel Hernandez and Tom Ince early in the second half to try and inject more attacking flair to their game.
However, they continued to struggle to make inroads into the Leicester defence, with the visitors looking more of a threat on the counter-attack.
A swift move between Jeffrey Schlupp and Mahrez created a chance for substitute Chris Wood, only for the striker to volley over McGregor's crossbar.
Hull felt they had a way back into the game with 15 minutes to play as Hernandez's flick brushed Wes Morgan's arm inside the penalty area, but referee Phil Dowd waved away their appeals.
Bruce's side laid siege on the Leicester goal in the closing minutes but they were twice denied by the woodwork as Livermore and Hernandez struck the post.
Both sides were reduced to 10 men in the final minutes as Konchesky and Quinn were shown red, the latter's dismissal easing the pressure on Leicester after Hernandez skied an effort from four yards, providing a timely boost for Pearson and keeping Hull mired in the battle at the bottom.