The home side should have opened the scoring after just three mins when Ryan Smillie rounded the visiting keeper and laid the ball in to the path of Ian Watt but his strike partner blasted the ball over the bar.
The visitors from Newmains showed they were not going to be pushovers when they themselves and the ball was laid left but ended with the same fate as Rovers when the ball was blasted over.
The 24th min saw an excellent piece of refereeing allow Watt a chance from what looked to have been an offside position after the Newmains keeper fumbled the ball but his net bound effort was blocked before being cleared.
Rovers eventually took the lead in the 33rd minute when they won a free kick on the half way line which Mark Weir played towards goal the ball was headed on by Dean Kindlan to Gordon Murphy who had a bit of work to do on the left before he played the ball across goal where Smillie was on hand to tap home for 1-0 to Carluke.
Carluke looked to extend this lead in the run up to half time and almost did when great link up play between Smillie and Murphy ended with the ball being played to Watt on the right, his cross ended with Smillie who had a shot saved before the ball fell to Murphy who had a low netbound effort cleared off the line.
Half Time Carluke Rovers 1 v 0 Newmains.
The second half saw Rovers continue to press for another goal and they eventually got this in the 54th minute courtesy of yet another foul on Mark Haddow 20 yards out, Weir took charge of the kick and blasted the ball home for 2-0.
Rovers did have to be on their guard as the game wore on and Newmains did have chances but the Carluke defence were up to all they threw at them with Jonny Grier making a telling save and Haddow blocking another effort to keep their lead at 2-0.
The scoring was wrapped up in the 79th minute when another sub Daniel Kindlan went on a run down the left leaving defenders in his wake before putting in an excellent cross which was hammered home by an onrushing Watt for a great third goal for Carluke.
This proved to be the last scoring in the match and Carlukie progress to the third round of this competition.
Grier, Souter, Murray, Gow, Haddow, Stewart(Dickson), Dean Kindlan(Wilson), Murphy, Weir(Dan Kindlan), Watt, Smillie