Substitute Chris Maguire dispatched a late penalty to settle matters in Group 10 after Albania had appeared more threatening at the Ruzhdi Bizhuta Stadium.
Scotland, who only just failed to reach the play-offs for this summer's finals, resisted the first-half pressure from the home side before starting their campaign in perfect fashion when Maguire kept his cool from the penalty spot with just five minutes remaining.
Although there were few chances in the first 45 minutes, Albania held the upper hand with Ditmar Bici, Jahmir Hyka and Enco Malindi constantly testing the visiting defence, while David Goodwillie and James Murphy called goalkeeper Shpetim Mocka into action at the other end. Scotland provided more thrust after half-time, particularly following Maguire's introduction on 67 minutes, and took advantage by scoring from their best opportunity when the substitute was felled by Mocka and stepped up himself to confirm the victory.
"I am very happy with the win," said Scotland coach Billy Stark. "It was the first match and we didn't know much about the Albanian side. They played well in the first half and had a few clear chances, as we did, but in the second half we played better – well enough to score one goal and win." Albania coach Artan Bushati said: "This is the best Albanian side we had and we put the best possible players on the pitch. We played well for the most part but lost sight of the game in the last few minutes and paid for it."