Scotland came out firing after the break with Darcy Graham scoring their only try with Wales forced to put in a monumental defensive shift to close the game out.
Gatland was delighted with the character shown by his side who were forced to make 160 tackles in the second half alone.
Wales’ final game will be at home to Ireland at Principality Stadium on Saturday.
“In the past we wouldn’t have absorbed that pressure and we would have cracked,” said Gatland.
“The players have shown tremendous character to win that game. We had a good first half and felt comfortable, but in the second half we couldn’t get out of our own half and there was a bit of inaccuracy.
“There were a few occasions where they were pressing and we were driving them back 10-15 metres and got a turnover. They were big moments. We’ve got a dream and now we’ll start planning for next week.”
No man typified Wales’ resolve and defensive steel in Scotland better than the official man of the match Hadleigh Parkes.
The Scarlets centre was outstanding both in attack and defence and is chomping at the bit ahead of next weekend’s enormous encounter with Ireland.
“We played pretty well in the first half and probably could have got a few more points,” said Parkes.
“Scotland really chucked everything at us in the second half and they played outstandingly well. They could have scored a couple of tries themselves.
“The spectators probably enjoyed it so as long as they enjoyed it that’s the main thing. The forwards defended very well.
“It was a real team performance and one which we had to dig deep for. It’s awesome to be in this position.
“The feeling in the team is amazing at the moment. We’re really enjoying each other’s company and we enjoy coming to training.
“We work hard for each other. Next week is really exciting.
“It’s going to be an amazing time for all of us in our careers and it doesn’t come along very often so we have to look forward to it.”
Despite being pleased with victory in Scotland, Wales captain Alun Wyn Jones has warned his players they will have to be better against Ireland.
“We knew we were going up to Murrayfield for a tough challenge,” he said.
“Back in 2017 they did a job on us and they almost did the same in the second half. Possession was probably 50/50, but they had the lion’s share in the second half.
“In previous games we’ve finished stronger. We thought we started well, but we definitely didn’t win that second half.
“We got pinned back in our 22 by penalties, but it was a magnificent defensive effort today.”
