Rovers were slow to start the match and fell behind in the 6th min when Neilston broke through a static Carluke defence and McKay rounded keeper Jonny Grier before slotting home for 1-0 to the home side.
This opener was almost added to a couple of minutes later with a shot from distance but Grier despite slipping on the heavy park managed to turn the ball round the post.
Rovers first chance of note came in 16 mins when a corner was played in and Stevie Murray controlled the ball well and laid it off to Scott Burns who in turn fed Jamie Dickson on the right but Dicksons shot came off the post and went harmlessly across goal.
The visitors drew level in the 21st minute with a well worked goal when Burns played the ball wide to Ian Watt on the right and after beating a couple of opponents he put in an excellent cross withy Murray connecting with a low diving header at the back post and his pinpoint effort was wide of the home keeper for 1-1.
Carluke were pressing their hosts back at this point and played some good football before taking the lead in the 31st min, Dickson won a free kick wide on the left and Watt fired in from all of 30 yards wide to the keepers left with a decoy run from Mark Haddow doing enough to put the keeper off.
As half time approached Watt and Dickson linked well on the left before Dickson cut in to the Neilston box and his effort looked to be net bound until it was cut out by a defender at the expense of a corner.
The second half saw what looked to be a slow start from Rovers turn in to an almost non start with Neilston having all of the play attacking up the steep slope.
With Rovers wasting passes and allowing Neilston almost total possession it meant they were limited to hitting on the break, the best chance they got came in the 87th min when Chick McCole broke at pace from midfield but with options on either side in a three on one situation he got bogged down on the edge of the Neilston box and the chance was lost.
The last chance of the match came in stoppage time when a loose ball after a corner was shot towards the Rovers goal but scraped the bar as it went harmlessly over and Carluke held on to pick up three vital points.
Grier, Bellew, Murray, Burns, Wilson, McDougall, Haddow, McCole, Dickson(Ward), Watt, Smillie.