"That was probably one of the most amazing games I've ever been involved in as a player and a coach," said Gatland.
"I've been on the other end, where you've lost in the last minute, so to come back like we did showed fantastic character.
"I know the Scots will be hugely disappointed but what a great advertisement for the game."
The dramatic finale reduced Scotland full-back Chris Paterson's feat of becoming his nation's first player to reach 100 caps to a mere footnote in the match.
Paterson's memory of his century will certainly be marred by the painful defeat, an early injury that saw the 31-year-old last less than half-an-hour, and a worrying back injury to team-mate Thom Evans that saw the wing rushed to hospital on a stretcher.
Scotland ensured the game had every chance to catch light by taking the game to their hosts in the opening exchanges.
Gatland hails Welsh determination
Perhaps the quality and accuracy was not always of the highest order, but the intent to score and entertain from both sides was evident from the first whistle.
Gatland had suggested before the game that opposite number Andy Robinson would seek to play a largely kicking game having picked Dan Parks at fly-half.
That theory and Scotland's unwanted record of scoring just one try in their previous five internationals were laid to rest within the first 20 minutes.
First John Barclay crashed over with a full-blooded charge that saw the Glasgow flanker buck off the attentions of James Hook and Gareth Cooper.
Then Parks scuffed a delicate grubber-kick behind the over-extended Welsh defence for a flying Max Evans to dive on.
As good as that opening was, it still did not hint at the drama that would unfold in the closing moments of the match.
Wales were trailing 24-14 when the game turned on Scott Lawson's 74th-minute sin-binning, as referee George Clancy finally lost patience with Scotland illegally slowing down Welsh possession.
But it took three precious minutes for Wales to break through a Scotland defence that had already been weakened by injury and was now a man light.
Heartbroken Parks fumes at 'injustice'
Leigh Halfpenny made the most of the extra space on the right wing to reach the corner, with Stephen Jones kicking the conversion to bring Wales within three points.
Down ticked the clock and in the final minute Lee Byrne, already the scorer of one try, burst through with only Phil Godman to beat, bringing the whole stadium to its feet.
Wales full-back Byrne chipped over the last defender but went sprawling as he made contact with Godman's leg.
Referee Clancy saw it as deliberate and yellow-carded Godman, though Scotland coach Robinson was adamant afterwards it was accidental.
Whether it was a trip or simply one player running into another, what was irrefutable was the rise in tension levels that were already twisting nerves to screaming point.
Wales captain Ryan Jones asked his fly-half Stephen Jones to boot them level from the penalty, having checked with the officials that there was time to restart the match and go for the win.
That decision proved inspired as Wales regained possession, laid assault against Scotland's 13 men and with no time remaining on the clock carved out the space for wing Shane Williams to go under the posts.
"I suppose that put my head on the block didn't it!" said a grinning Wales captain Jones afterwards.
"The referee said we had time for more rugby, even though it was a matter of seconds. We knew we had time to get the ball back and play some phases.
"I thought 'let's get the points and take the pressure off', because momentum had firmly come our way.
"And we practiced all week on scoring from the kick-off, didn't we and it paid off!
"Any more like that and I'll be as grey as Warren Gatland or as bald as Shaun Edwards I expect!
"It's the decisions you make and you live or die by them and there are very few opportunities in your life when you get to make those, and live them out in front of 80,000 people.
"It's exciting but don't get me wrong, it's a huge relief when it pays off."
Wales and Scotland produced a dramatic finish at Cardiff
Scotland coach Robinson agreed it had been a special game, although understandably his feelings differed from the victors.
"I don't think I've ever felt like this in any game I've ever been involved in," said the former England head coach.
"There's mixed emotions and I've got to say I think the Scottish players did their country proud today in the way that they played the game."
Robinson was right to emphasise his players' part in the spectacle, for it takes two sides to reach the heights of entertainment.
Both sides now have a fortnight's rest before their next encounters, where Wales will try to derail France's Grand Slam charge in Cardiff while Scotland go to Italy seeking their first win of the championship.
If either side can get close to replicating their Millennium Stadium encounter on Saturday, it will be compulsive viewing.
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