Zebre had taken the lead when No.8 Dries van Schalkwyk ran on to an inside ball from Josh Sole and forced his way under the posts for a converted score.
Twice Edinburgh got the ball over the whitewash only for both Laidlaw and Greig Tonks to be held up over the line.
They weren't made to pay for their profligacy, however, and Scott - who has taken temporary charge with Duncan Hodge after the departure of coach Michael Bradley - paid tribute to Edinburgh's resolve in difficult conditions.
"We had enough opportunities to win that game comfortably tonight but a couple of silly, individual errors and poor decisions kept them in the game and kept the pressure on us but, let's be clear, I'm happy with the performance towards the end, we dug deep where poor discipline could have cost us the game," said Scott.
"I think we had about 70 to 80 per cent of the ball and dominated large parts of the set piece but the most pleasing thing was the way we worked to grind out the win.
"We were unfortunate to have two tries held up where, on a fast, dry pitch I'd have backed us to score, and these small margins are what made the game close in the end but the overriding emotion is that we're happy to be leaving here with a win."
Extensive in-game highlights of the RaboDirect PRO12 are now available on the official YouTube channel.
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