The series started off 1-1 after the first two opening tests, but the Lions held the lead for the rest of the game after that, CNN reported.
"We fronted up today and I think the scoreline reflected it and we represented the four countries with pride," Lions skipper Alun Wyn-Jones said.
The Lions held a 19-3 lead at halftime, but two penalties from Christian Lealiifano early in the second half narrowed their lead to three points.
"We wanted to win the collisions and breakdowns. It was always going to come down to that today. They came back at us in the second half and we came back pretty well," Wyn-Jones said.
It was an outstanding performance. We started well, came under some pressure and bounced back," coach Warren Gatland added.