And all that on the back of a heart-breaking late defeat in the second rubber just seven days earlier when momentum appeared to have been heading the hosts' way.
"We spoke about being prepared to go to a place that not many players go to in terms of being able to push your body to the limit. The players did that, they ran themselves into the ground," said Gatland.
"It was an outstanding performance. We started well, came under pressure and then bounced back. I said all along that Australia were desperate last week and brought everything they had to the table but we always felt there was another step up in terms of what we could bring. We felt there was another level emotionally, another couple of levels in us, and we were able to produce that tonight.
"These guys have done themselves proud, they've done that jersey proud and they deserve a huge amount of credit for that performance and for what they've achieved. And we said in the changing rooms afterwards, it's not just been the 23 players, it's been the whole squad. The management and the medical team have done a brilliant job, the support staff, they've been exceptional both on and off the field. The players and the people involved have to enjoy this moment."
Having led 19-3 just seconds before half-time, the Lions were pegged back to 19-16 after six minutes of the second period before kicking on to claim a record points tally in 125 years of touring.
And in addition to making the last quarter a little more comfortable to watch than the first two Tests in Brisbane and Melbourne, Gatland felt the manner in which his side breached the Wallabies defence was just reward for their efforts and intentions throughout the 10-match adventure.
"I'm really pleased that the players finished off what was a fantastic series. We've played some great rugby on this tour. We were able to put it together tonight, particularly in the second half," added Gatland.
"We came out here with the attitude that we wanted to play some rugby, we wanted to move the ball. We'd scored a lot of points and a lot of tries here and four tries tonight was a vindication of how we well we've played overall on this tour."