Mahrez headed the Foxes in front after five minutes and fired in calmly for his second, although he seemed offside.
Swansea’s Ki Sung-yueng headed against the bar after the break, but Mahrez finished an incisive counter-attack to seal his first ever hat-trick.
Manchester City’s defeat by Stoke sees Leicester leapfrog them at the summit.
This result leaves the Swans, 15th in the league, four points above the relegation zone, having won only one of their last 11 league matches.
Manager Monk’s position had already been under intense scrutiny and, having heard his side booed for a second successive home game, there will be more doubts than ever about his future.
Riyad Mahrez was ever-present for Leicester, receiving plenty of possession on the right and making dangerous runs into the box
The pre-match attention was inevitably focused on Leicester’s Jamie Vardy, who had set a Premier League record by scoring for an 11th successive game against Manchester United.
But the former Fleetwood striker had to settle for a supporting role as Mahrez took centre stage.
Both the Algerian’s first two goals were fortuitous, but they were no more than Claudio Ranieri’s side deserved for an utterly dominant first half.
Mahrez’s opening goal was a scrappy one, the ball flicked on from a corner and appeared to hit his head and arm before trickling over the line.
The 24-year-old’s second was a more conventional finish – confidently swept into the bottom corner – but he seemed to be offside from N’Golo Kante’s pass.
Piling the pressure on Monk
Monk said his players were affected by the “tension and anxiety” of the Liberty crowd when they fell behind 2-0 to Bournemouth a fortnight earlier.
But whereas the Swans recovered to draw 2-2 against the Cherries, they looked like cannon fodder for Leicester.
Centre-backs Ashley Williams and Kyle Bartley seemed nervous, the latter needlessly conceding a corner for the opening goal and presenting Vardy with a glorious chance to score for a 12th successive game.
Garry Monk (left)
Monk said his team was ‘extremely poor’ and added that they would have to find a solution ‘very soon’
Their unease extended to the rest of the team, with Swansea struggling to keep possession or create any opportunities of note.
And it will have been the dismal performance as much as the result which will compound the concerns of an already worried Swansea board.
Leicester’s unlikely title challenge
Manchester City’s defeat to Stoke had presented Leicester with the opportunity to reclaim their place at the top of the table and, as Ranieri’s men have done so often this season, they seized the moment.
The Foxes were barely tested by a dreadful first-half showing from Swansea, but they were incisive and clinical when they needed to be.
Monk’s men posed more of a threat after the interval, with Ki heading against the bar and Gylfi Sigurdsson’s whipped shot hitting the post.
But Leicester were still in control and they eliminated any slim chance of a Swansea revival when a swift counter-attack involving Leonardo Ulloa and Vardy was finished by Mahrez’s low, firm shot.
Leicester are now two points clear at the top of the table and, with the busy festive period looming, they find themselves in the unlikely position of being early title challengers.
Man of the match – Riyad Mahrez
Riyad Mahrez
Mahrez has been crucial to Leicester’s success this season, as demonstrated by this clinical hat-trick which took his campaign tally to 10 league goals
What they said
Garry Monk says he is ‘frustrated’ at poor results
Swansea manager Garry Monk: “It was a poor first half from us. Those first two goals were extremely soft. The first one was clearly handball, the second was clearly offside, but the results haven’t been good enough in this period.
“I feel sorry for the fans. We’re not playing like this club can play, like these players can play.
“It’s very difficult to analyse and put your finger on it. The results aren’t acceptable and I’m fully aware of that, and it’s up to me to put it right.”
Swansea 0-3 Leicester: We played very good football – Claudio Ranieri
Leicester manager Claudio Ranieri: “We are thinking about ourselves, to take points and make good football. That is our first goal, to achieve 40 points, to be safe.
“It was a tough match because Swansea play very good football. We started very well, we scored three goals, and had a minimum other four clear chances and I’m very pleased.
“Our fans they must dream, but we must stay calm and keep our feet on the ground.”
The stats you need to know
Riyard Mahrez becomes the first Algerian player to score a Premier League hat-trick.
Mahrez has now been involved in 16 Premier League goals this season (10 goals, 6 assists) – a record only team-mate Jamie Vardy can match (14 goals, 2 assists).
The midfielder became only the third Leicester player to score a Premier League hat-trick, after Ian Marshall and Stan Collymore.
The Swans have won just one of their last 11 Premier League games (D3 L7).
Meanwhile, the Foxes have lost just one of their last 19 top-flight games (W12 D6).
Claudio Ranieri’s side are the only team to have scored in all 15 games this season.
What next?
Leicester face a tricky run of fixtures, with Chelsea their next league opponents – followed by away trips to Everton and Liverpool – but on recent form they have proved they are capable of competing with the best. Swansea, meanwhile, desperately need a league win, though their next match is away to title contenders Manchester City.
Premier League Results
Stoke 2 – 0 Man City FT
Arsenal 3 – 1 Sunderland FT
Man Utd 0 – 0 West Ham FT
Southampton 1 – 1 Aston Villa FT
Swansea 0 – 3 Leicester FT
Watford 2 – 0 Norwich FT
West Brom 1 – 1 Tottenham FT
Chelsea 0 – 1 Bournemouth FT
(BBC Sports)
