Cliftonville stay top of the Premiership table after this win at Ballyskeagh.
But Reds manager Tommy Breslin will not have been to happy with his sides showing.
There was little happening in the first half as both sides tried to get to grips with each other.
Martin Donnelly had a free-kick in the 31st minute but it was easily saved by keeper Lee Windrum and the half ended scoreless.
The second half was a lot brighter than the first as the Reds took the lead in the 52nd minute.
A through ball found Liam Boyce and he finished well.
Distillery had a good chance two minutes later. Ryan McCann found Gary Liggett but he shot wide.
It was 2-0 in the 70th minute as Barry Holland finished after Distillery failed to clear a cross.
Then home side did pull one back when Gary Liggett shot home from the edge of the box.