Scotland, in their first competitive match under new coach Gordon Strachan, took the lead just before half-time when defender Grant Hanley knocked in a corner from Charlie Mulgrew.
Robert Snodgrass went close to making it 2-0 when his curling left-foot shot from the edge of the penalty box struck the post in the 54th minute.
Wales had a goal by substitute Andy King chalked off for a foul on keeper Allan McGregor before Aaron Ramsey levelled with a ferocious 72nd-minute penalty that went in off the underside of the bar.
The spot-kick was awarded after Snodgrass was sent off for a reckless challenge on Chris Gunter on the edge of the area.
Hal Robson-Kanu put Wales 2-1 up less than two minutes later, nodding his first international goal following a right-wing cross by King.
Ramsey's night was spoiled when he was dismissed in stoppage time for a professional foul.
Tottenham Hotspur forward Bale, who had been an injury doubt before the match, was replaced at the interval by debutant Jonathan Williams.
The victory lifted Chris Coleman's Wales side to third in the table with six points from five matches. Scotland are rooted to the bottom on two points.
Belgium and Croatia lead the way on 13 points.
