Carluke started well and pressed Maryhill back early on and took the lead in 5 mins when Ryan Smillie won a free kick on the left after chasing what looked to be a lost cause ball, Ian Watt elected to take the free kick and lofted it over the head of the visiting keeper from all of 30 yards for 1-0.
Maryhill were dangerous on the break but there first effort went wide of target in 10mins.
Watt and Smillie continued to link well and in 13 mins Smillie saw his ball across the face of goal have no takers and another chance was lost.
Rovers thought they had increased their lead in 16 mins when Mark Weir floated another free kick in and Mark Haddow rose to head home but the referee gave an off side decision in favour of Maryhill.
Rovers best chances continued to come from the many free kicks Maryhill gave away and in 18 mins Weir saw an effort from 35 yards tipped away for a corner which ended with a Jamie Dickson effort going over the bar.
Carluke doubled their lead in 25 mins when Weir played an excellent ball to Watt on the right and after outstripping the Hill defence he played a low ball across goal to give Gordon Murphy a chance he could not pass up at the back post for 2-0.
The second half saw Carluke very slow to start with Maryhill pressing them back with wind advantage, the visitors were good on the break and won a free kick in the 55th minute that was rattled off the bar before the ball was blazed over the bar.
Maryhill then had a golden chance in the 57th min as the home defence were posted missing but the end header was wide of target.
After being pressed back for long periods by the visitors Rovers hit on the break in the 73rd min when good work across the middle of the park ended with Watt setting Smillie free on the right and as he homed In on goal he let loose a low shot across the keeper that found the corner of the net for 3-0.
This goal seemed to break the spirit of Maryhill and it took them until the 88th min to make another chance which resulted in their consolation goal when they were allowed to push the Rovers defence back before a long range shot was well saved by home keeper Jonny Grier only to see the loose ball fall kindly for Maryhill to score from close range for 3-1, a score that held until the end of the match.
Grier, Souter, Murray, Gow, Dickson, Haddow, Murphy, Dean Kindlan, Weir, Watt, Smillie.
Subs Lithgow for HAddow, Wilson for Dickson, Cavanagh for Smillie