The Reds faced struggling Donegal Celtic in their game at Solitude, but will feel relieved to have picked up all three points after a spirited display by the visitors.
In fact, it was DC who started the game the stronger, but they failed to convert that spell into goals.
Cliftonville took the lead in the 34th minute when visiting goalkeeper Niall Murphy could only parry Stephen Garret's shot back into the midfielder's path after he had embarked on a defence-splitting run.
Pat McAllister's side found the equaliser 12 minutes after the break though, when Ryan Deanes converted from a Kevin Hughes pass.
However, Cliftonville grabbed the winner five minutes from time with Ciaran Caldwell directing a header past Murphy from Ronan Scannell to seal the points.
Crusaders also won on Saturday to ensure there was no widening of the gap between first and second in the table, as they secured a 3-1 win away to Coleraine.
Eamon McAllister was the hero for the Crues with two goals, the first coming just four minutes in as he lashed a first-time shot on the volley past Michael Doherty.
Curtis Allen equalised for the hosts when he headed in a David Scullion cross in the 27th minute, but Timmy Adamson restored his side's advantage with a brave header before McAllister completed an impressive brace with an effort into the top corner.
In the game at Windsor Park, Linfield all but surrendered their already faint hopes of overhauling the top two as they were held to a 1-1 draw at home to Lisburn Distillery.
With the visitors holding the Blues scoreless for the whole of the first half, Michael Gault opened the scoring in the 50th minute when he curled a shot from the edge of the area.
However, Aaron Boyd equalised 16 minutes later and although the Whites lost David McCullough to a second yellow card late on, they had already done enough to seal what could prove to be an invaluable point.
Elsewhere, Ballinamallard boosted their chances of a top six finish with an impressive 4-0 victory over Dungannon Swifts.
Jason McCartney opened the scoring for the Mallards in the 24th minute, and added a second just after the hour mark, before completing his hat-trick with a superb long-range volley.
Andy Crawford latched on to an incisive through-ball to slot home the hosts' fourth, and Whitey Anderson's side now just need one more win before the split to confirm their top-six status.
In the mid-Ulster derby, it was Portadown who took the bragging rights with a 3-1 win over Glenavon at Shamrock Park.
Sean Mackle showed an impressive turn of pace to burst into the visitors' penalty area and home in the 13th minute, before a wonderful effort from Darren Murray saw him lob Davy O'Hare in the 40th minute to double his side's advantage.
The hosts were making good use of the long ball and the tactic contributed to the Port's third of the afternoon when a hefty clearance resulted in Kevin Braniff steering the ball into the net.
The Lurgan Blues pulled one back when Ciaran Martyn pounced on a defensive mistake and converted from close-range, but Glenavon had too much to do to turn it around and the Ports held on for a deserved victory.
Meanwhile, at the Ballymena Showgrounds, Ballymena United played out a goalless draw with Glentoran.
Danske Bank Premiership results:
Ballinamallard 4 - 0 Dungannon Swifts
Ballymena United 0 - 0 Glentoran
Cliftonville 2 - 1 Donegal Celtic
Coleraine 1- 3 Crusaders
Linfield 1 - 1 Lisburn Distillery
Portadown 3 - 1 Glenavon