Trinidad star Collin Samuel opened the scoring goal Saint Johnstone and with the Saints controlling the bulk of the first half it looked like they might reach the break in the lead.
But Kris Boyd levelled in 40 minutes, slightly against the run of play.
Still the home side had chances to win it but with seven minutes remaining Sasa Papac curled home a late clincher.
St Johnstone boss Derek McInnes: "I felt we had the better chances in the game, we went toe-to-toe with a very good side.
"They are champions, they are used to winning and that is why they keep going.
"We were a bit sloppy at both goals. We played a part in our own downfall. We are learning as we go along, we are progressing.
"These games won't dictate where we finish this season. On today's performance, we should have got something.
"The goals changed the reflection of the game. We're creating chances, we look a real threat. You don't always get what you deserve."
Walter Smith was a relieved Gers boss.
''We're obviously pleased to have fought back and won the game. It's the type of game I fully expected to get.''
Smith recognised that St Johnstone used their tall players to good effect, but said: ''They played some good football as well, and having the extra man in midfield helps them in that respect. Over the piece we're just delighted to get the win.
''I'm happy today that after winning our previous Old Firm game at Ibrox we've managed to win away from home.''