Colin Slater’s men had to come from behind on Saturday at Tileworks Park in Stonehouse when Greenock broke the deadlock after 16 minutes.
However, parity was restored just after the second half restart when Ian Watt was the first man to react after a parry from the Greenock goalkeeper.
And Carluke quickly went in front when Ryan Smillie was upended in the box for a clear penalty; Mark Weir expertly converted.
Rovers had other chances to score but couldn’t get the goal which would have made the game secure. But despite Greenock having a couple of chances near the end Carluke held on and will play the winner of tonights clash between Wishaw or Blantyre Vics in the quarter-finals.
Meanwhile Robert Irving’s Lesmahagow finished their league season with a 0-0 draw against Renfrew