The first chance of the game fell to the Light Blues after just five minutes, with Fraser Aird playing a ball into the Warriors' box in a bid to set up Nicky Law, but the 26-year-old was unable to get on the end of it.
Two minutes later, the home side nearly broke the deadlock when Ben Greenhalgh got on the end of a low ball from the right-hand side, but the Gers keeper was able to smother with ease.
Eventually, the Old Firm outfit took the lead when Smith unleashed a shot from the edge of the box just after the half-hour mark.
Just four minutes later, Dean Shiels doubled his side's advantage with a composed finish following a threaded ball from Law.
In the second half, the home side made things even more difficult for themselves after Robert Duncan conceded a penalty and was sent off in the 65th minute.
Lee McCulloch made no mistake from the spot to put his side three goals up.
Greenhalgh had another chance to strike for the Warriors a few minutes later, but his free kick soared wide of the post.
Rangers then made it four in the latter stages of the game when Law struck from distance to net his side's 100th league goal this season.