The success sees Scotland overtake Wales to move into fourth position, while Croatia will progress onto the playoffs next month.
Here, Sports Mole analyses the game to see if the points went the correct way.
On target 4
On target 3
Was the result fair?
Despite Croatia having the better of possession and having more efforts on goal, this was a deserved result for Scotland. Their home form has left a lot to be desired over the past 18 months but they were more than a match for their higher-ranked opponents.
Scotland manager Gordon Strachan would have been eager for his side to put on a show in front of their home supporters to try to build some momentum ahead of the start of next year's European Championship qualifiers. There are another 11 months until they begin, but Strachan will be content in the knowledge that his squad of players can perform against quality opposition.
Croatia dominated possession on occasions while also creating 16 opportunities, but their travelling fans would have been disappointed with their countrymen this evening. Apart from Pletikosa, none of them can come out of this fixture with much credit.
Sports Mole's man of the match
Scotland's performance was based around a collective effort rather than a stand-out performance but after playing his part in both goals, Anya deserves the man of the match accolade. He hasn't been on the international scene for long, but he has already established himself as Scotland's leading player on the left-hand side.
It was hardly a gaffe, because Naismith netted the rebound, but Barry Bannan would have been disappointed not to have scored his first goal for his country. Credit has to be given to the goalkeeper, but the Crystal Palace is unlikely to get a better chance to open his account.
Referee Ovidiu Hategan had a quiet game, and made the correct decision to award Scotland a second-half penalty. It only all referees could officiate games like this man!
Scotland: Scotland have 11 months of friendly action to contend with before they can attempt to qualify for Euro 2016, but depending on their draw, this performance would suggest that they are improving under Gordon Strachan.
Croatia: Croatia must await the draw for the playoffs to see who they must face to qualify for the finals in Brazil. It's arguable that their performance this evening was a result of wanting to avoid any injuries or suspensions ahead of next month, but coach Igor Stimac has a lot of work to do to get his team in a positive frame of mind.