Crusaders remain in second place after a late goal earned them a 1-0 victory over a 10 man Portadown side at Seaview.
Linfield are suddenly back in the title race, 10 points off the pace, after a superb display against Tommy Breslin's team.
Two goals in quick succession in the first half from Matthew Tipton put the Blues firmly in the driving seat.
But a well taken effort from Liam Boyce - his 21st goal of the season - gave the Reds fresh hope going into the second half.
However an unselfish piece of play from Mark McAllister, who had earlier been denied by Cliftonville 'keeper Conor Devin, set up a third goal for Linfield nine minutes into the second half.
McAllister had a chance to shoot but instead he slipped the ball to Michael Carvill who was left with a simple finish.
Blues goalkeeper Alan Blayney was forced into a couple of smart saves in the closing stages of the game but Linfield held on for a crucial three points.
At Seaview it took a late goal from Gareth McKeown for Crusaders to defeat Portadown, who had Keith O'Hara sent off for a second bookable offence in the 84th minute
McKeown struck the winner within 60 seconds as his right-footed effort flew into the net after he was set up by Paul Heatley.
A late equaliser from sub Shane Jennings earned Coleraine a share of the spoils from a 1-1 draw with Glentoran at the Showgrounds.
Marcus Kane had put the Glens ahead on the stroke of half time with a long range effort before Jennings fired home with a few minutes left.
Donegal Celtic have opened up a four point gap at the bottom of the table after beating Glenavon 1-0 while Lisburn Distillery lost 2-0 to Ballinamallard at Ballyskeagh.
Paul McVeigh hit the only goal of the game at Celtic Park in the 58th minute while two goals in the final quarter secure the Mallards victory over the Whites.
Shortly after Gary Liggett had missed a good chance at the other end Jay McCartney gave the visitors the lead in the 77th minute when he scored form close range.
Less than two minutes later McCartney turned provider when his cross was met by David Kee who headed home with the aid of the crossbar to pile more misery on Tim McCann's side.
IFA Premiership Results: Tuesday 1 January 2013
Coleraine 1-1 Glentoran
Coleraine: Shane Jennings (79)
Glentoran: Marcus Kane (45)
Crusaders 1-0 Portadown
Crusaders: Gareth McKeown (85)
Portadown: Keith O'Hara (S/O 84)
Donegal Celtic 1-0 Glenavon
Donegal Celtic: Paul McVeigh (68)
Linfield 3-1 Cliftonville
Linfield: Matthew Tipton (20, 23), Michael Carvill (54)
Cliftonville: Liam Boyce (34)
Lisburn Distillery 0-2 Ballinamallard United
Ballinamallard United: Jason McCartney (78), David Kee (79)