The Fulham forward, on loan at Northampton, drove in an angled finish for a fine solo effort then headed home from a Max Johnston cross.
Liverpool winger Ben Doak drilled in a penalty on 32 minutes, with Barnabas Kovacs replying before half-time.
A good evening for the Scots was marred by a late red card for Johnston.
The Sturm Graz full-back, returning to the home of former club Motherwell, picked up a second booking for a mistimed tackle in stoppage time.
Bowie’s opener came after just two minutes as he powered forward from his own half and cut in from the left, holding off two challenges, before sliding the ball into the bottom corner.
Soon after, he rose well to steer in a terrific first-time cross from the galloping Johnston.
Doak had teed up Johnston on that occasion and those two linked again for the penalty as the 17-year-old was upended by a clumsy challenge.
A dominant display was interrupted when a corner was prodded home from close range at the second attempt by Kovacs.
The second half was played at a much reduced pace, with a thunderbolt from centre-half Ibane Bowat the closest the hosts came to adding to their lead.
Scotland, who lost their first match of this campaign away to Spain, face Malta at the same venue on Tuesday.
Source: BBC
