Wales had led 7-0 early on in the first-half after an early Gareth Davies try, but Scotland recovered to hold a slender 13-10 advantage at the interval.
The hosts recovered to prevail 27-23 through tries from Jamie Roberts and George North. Although Gatland was pleased to claim a first win of the tournament he admitted that it was a difficult Test match.
“I think it was a tough game, we had to dig deep and grind out a victory,” he said.
“There is no easy game in this tournament and we have seen improvement of all the teams in this competition.
“We had to use everything we had in the tank to win, the six-day turnaround was tough and the impetus from our bench really helped us.”
Regarding the tactical aspects of the game, Gatland was pleased by the strength of his team’s set-piece, before praising try-scorers Roberts and North.
“Both teams ran really hard at each other and Scotland made the breakdown really tough for us. I think our set-piece in terms of line outs and scrums was excellent, our maul defence was good.
“We had a couple of chances and we took those chances, once from Jamie Roberts who was deservedly man-of-the-match.
“Jamie was outstanding as he was last week too, and we saw something special from George North. Sometimes you need that something special in games and I thought we got stronger as the game went on.”
Wales captain Sam Warburton also expressed his delight at seeing both Roberts and North score within five minutes of each other to allow Wales to recover from 16-13 down to win.
“When you look back over the last 4-5 years our backs have been outstanding in the big games Jamie and George are two of those, they were great today and are both such incredible athletes.
“At any moment in the time they can produce something special and they did today. When they play well they are very difficult to stop and I’m really pleased for them both, they are two very valued world-class players.”
Wales are in action again at Principality Stadium in two weeks’ time where they will face France, who are currently chasing a Grand Slam after defeating Italy and Ireland.
Warburton added: “It will be another tough game and I’m sure France will want to come to Cardiff and beat us. We know how difficult it is to beat Ireland so we’ve got to give them a lot of credit for that, it is a very tough task.
“We have a pretty good record against them recently but they’re going to be a different side this time around.
“The six-day turnaround for us has been tough so it is good to have a couple of weeks until that one.”
