South Africa battled through a nervy final day in the second Test to claim a draw and win the two-match series 1-0.
Having resumed on 38-1 in their second innings, requiring a further 331 runs for victory, South Africa adopted a cautious approach to avoid defeat in a Test match dominated by the hosts.
Amla led by example, facing 159 balls during a gritty knock of 25, while Vernon Philander also contributed significantly with an unbeaten 27 off 98 deliveries as South Africa closed on 159-8 from 111 overs.
The series win takes South Africa back to the top of the International Cricket Council (ICC) rankings at the expense of Australia, but Amla - celebrating success in his first Test series as captain - played down the significance of that achievement.
He said: "That wasn't our primary aim to get to number one, it was to find a winning formula with a newish team and I think after the first Test - where we did manage to win - and the kind of character we've shown in this team I think we're certainly heading in that direction and finding a good formula for a winning team.
"I think Vernon, the way he handled [things] towards the back end of the game, he had a brilliant game all round. He bowled brilliantly and managed to shepherd the guys at the back end in a high pressure moment, he's been a high-pressure person for us for a while.
"Not many of us throw wickets away and the guys really dug deep, and they knew that to win a series here, we were going to encounter certain times where you will have to reach your breaking point. We almost reached that, and the guys hung in there and we managed to pull out a draw.
"It's not a tangible thing, it's a really pleasing thing, certainly being my first series as captain, I have enjoyed it immensely.
"To win here in Sri Lanka, not many foreign teams come here and do that and for us to have done it, I'm really thankful to the team for the amount of commitment they have put in."