Victory in Zagreb over Tuesday's opponents and in Macedonia last time out were the only times the Scots have secured three points in World Cup 2014 qualification, so it was important to finish on a high as new boss Gordon Strachan continues his rebuilding of the side.
And Robert Snodgrass, who was celebrating the birth of his baby daughter, gave his side the perfect start, heading in Charlie Mulgrew's cross just before the half-hour mark.
The Norwich man almost doubled the lead soon after, but saw Stipe Pletikosa brilliantly tip his low drive onto the post in the Croatia draw.
Despite their talented opponents possessing plenty of firepower, they never really created any clear-cut chances all evening, with Real Madrid star Luka Modric looking very much a forlorn figure on the Hampden turf.
And after the lively Ikechi Anya was felled in the box, Barry Bannan saw his penalty saved by Pletikosa, but Steven Naismith was on hand to took in the rebound to be sure of the points.
Scotland couldn't get near the ball in the opening stages with Modric very much dictating the tempo of the match in the middle of the park.
But for all their possession Croatia didn't really offer much of a threat, and they were made to pay for their profligacy in creating clear-cut chances as Strachan's men took the lead.
A loose pass from Croatia skipper Darijo Srna was cut out by Steven Naismith, who played the ball into the path of the onrushing Mulgrew, whose lofted cross was headed home from close range by the Norwich man.
The goal seemed to lift the home side, and if it wasn't for the reflexes of Pletikosa in keeping Snodgrass' drive out after a slick passing move, it could have been much worse for the visitors.
Croatia did come into the match more after the interval, but they could never really produce that final ball needed to unlock the home defence.
Former Arsenal striker Eduardo could have put his side back in it, but as he rounded the onrushing Alan McGregor his touch was too heavy, and he couldn't steer the ball into the empty net from the angle.
And with Igor Stimac's men pushing forward, Anya's footwork was too quick for Domagoj Vida, who brought the Watford man down, with the Romanian referee showing no hesitation in pointing to the spot.
Naismith was on hand to save Bannan's blushes, and it was nothing more than the hard-working Everton forward deserved after causing the visitors problem all evening.
The result means Scotland have now completed the double over Croatia who, due to results elsewhere, scraped a place in the play-offs, but it is Strachan who has a great deal to be positive about for the future.