George McMullan got the hosts off to the perfect start after just three minutes when he tapped in on the rebound after Ciaran Caldwell's effort struck the post.
The Whites equalised midway through the second half with a stunning 30-yard free kick from Andy Hunter, but Cliftonville's lead was restored when Joe Gormley rifled home in the 74th minute.
Martin Donnelly sealed the win when he swooped the ball over Distillery keeper Billy Brennan eight minutes from time.
In the game at the Oval, Portadown celebrated 25 years in management for boss Ronnie McFall with a 2-0 win over Glentoran.
In a game packed full of chances, it was Jamie Tomelty who broke the deadlock when he guided a header over Elliot Morris in the 69th minute.
Glentoran pressed for an equaliser but were caught on the break in injury time when Kevin Braniff netted from close range.
The result means that Portadown remain well in touch with the top two in the league, with the Glens well adrift in fourth.
Elsewhere, struggling Glenavon received a big boost as they secured a much-needed three points with a 3-0 victory over Ballymena United at Mourneview Park.
The hosts were boosted when Sky Blues lost Gavin Taggart to a second yellow card after 23 minutes, and Chris Laverty added insult to injury by scoring direct from the resulting free kick.
Mark Miskimmin netted in the 65th minute, and two minutes later Jay Magee scored from the spot after Miskimmin was fouled in the area by Chris Rodgers.
The win moves the Lurgan Blues off the bottom of the league, seeing them jump to 10th in the table.
Linfield maintained their four-point lead at the top of the table with a 1-0 win over Belfast rivals Crusaders at Seaview.
Mark McAllister scored the only goal of the game in the 27th minute when he finished from close-range after Crues keeper Sean O'Neill had saved from Phillip Lowry.
Coleraine edged out Dungannon Swifts 3-2 in a thrilling game at the Coleraine Showgrounds, with the Bannsiders opening the scoring with less than 30 seconds on the clock through Ciaran Clarke.
It was 2-0 ten minutes later when Curtis Allen's shot went in off the crossbar, before the visitors were handed a lifeline as Joe McCready pounced on a mistake by Coleraine keeper Michael Doherty.
However, Johnny Black restored the two goal advantage for the hosts when he scored from the spot just before half-time.
Terry Fitzpatrick reduced the deficit in the 68th minute when he met a Shea McGerrigan free kick, but Coleraine held on for the victory.
In Friday night's game at Seaview, Carrick Rangers fell to a 2-1 defeat at home to Donegal Celtic.
Eamonn McAllister opened the scoring for DC when he capitalised on hesitancy in the Carrick defence five minutes before half time.
Davy McAlinden restored parity with a great turn and shot in the 65th minute, but Jonathan Gowdy won it for the visitors with a fine header in the 87th minute.
IFA Carling Premiership results:
Saturday 10 December 2011:
Cliftonville 3 - 1 Lisburn Distillery
Cliftonville: McMullan 3, Gormley 74, M Donnelly 82.
Lisburn Distillery: Hunter 66.
Coleraine 3 -2 Dunagannon Swifts
Coleraine: Clarke 1, Allen 11, Black 45+2 (pen).
Dungannon Swifts: McCreadie 39, Fitzpatrick 68.
Crusaders 0 - 1 Linfield
Linfield: McAllister 27.
Glenavon 3 - 0 Ballymena Utd
Glenavon: Lavery 23, Miskimmin 65, Magee 67 (pen).
Glentoran 0 - 2 Portadown
Portadown: Tomelty 69, Braniff 89.
Friday 9 December 2011:
Carrick Rangers 1 - 2 Donegal Celtic
Carrick Rangers: McAlinden 65.
Donegal Celtic: McAllister 40, Gowdy 87.