Nathan Patterson scored his first ever Scotland goal, linking well with John McGinn in the first half, then the same duo combined to set up Che Adams for the second goal after the interval.
There were a few nerves when Patterson conceded a penalty but Craig Gordon produced the goods to save the spot kick with Kieran Tierney clearing the rebound with a fantastic response.
Now focus will be on the Denmark game and trying to ensure that Scotland are seeded for the play-off which takes place in March.
Player ratings scale - 10: One of the best performances you've seen. 9: Outstanding. 8: Very good. 7: Good. 6: Average. 5: Poor, 4: Very poor. 3: A terrible day at the office. 2: Abysmal. 1: One of the worst performances you've seen.
1. Craig Gordon - 8
Showed why he is the undisputed No.1. A terrific save in the first-half to deny Moldova captain’s Ionita, demonstrating his concentration and reflexes. Second half? Saves a penalty. Photo: Craig Williamson - SNS Group / SFA
2. Jack Hendry - 6
Moldova had some their best moments down Scotland’s right-hand side behind Nathan Patterson. But overall a solid performance. Photo: Craig Foy - SNS Group
3. Liam Cooper - 6
A largely faultless display from the Leeds United ace as he filled the Grant Hanley role. No nonsense at times. Photo: Craig Williamson - SNS Group / SFA
4. Kieran Tierney - 8
Showed exactly why he is so key to Scotland especially going forward. Constantly getting on the ball and driving forward. Produced a stunning tackle to deny Moldova a goal from a rebound from the penalty. Photo: Sammy Turner - SNS Group