Shane Williams scored twice but it was Wales' defence which proved the difference as they blunted a Scottish attack which had scored three tries in Paris last week.
Wales dominated the first 20 minutes with James Hook revelling in his return to the fly-half position and the visiting pack blowing away the Scottish scrum.
But after leading 16-0 Wales lost their momentum with yellow cards for Bradley Davies and Lee Byrne.
And Gatland will be concerned at the way Wales struggled to get hold of possession in the second half relying on their defence to seal the win.
"I thought we played better last week, we played really well. We were a bit unlucky," said Gatland.
"I thought we were clinical against Scotland, defended exceptionally well and thoroughly deserved to win.
"The performance needs to improve but the result was good.
"I thought the players could have easily lacked confidence as they have been under the pump but they continued to work really hard and front up.
"The lessons we learned from last week were pleasing. We showed great character to hold out for that ten minutes when we were down to 13 men, and that was the game."