Speaking after the game, Leinster out-half Sexton, who is getting married in Ireland next Friday, said that the squad always believed in their ability to bounce back from last weekend's disappointment.
"We knew that we had it in us. I suppose in the first couple of Tests we didn't get the ball off first phase really. We didn't get a chance to attack and I think we got a little bit more tonight.
"The scrum was pretty dominant and that gave us a lot of penalties which is always important. That's where we got our foundation from (because) we let them back into it, which was disappointing.
"But tthe way we bounced back was just outstanding. It feels like a dream to be honest. I remember these scenes from 1997 and you never think you're going to be a part of it.
"To be a part of the next team to do it is a dream come true."
The Lions built up a 19-3 lead as England prop Alex Corbisiero touched down before Leigh Halfpenny kicked four penalties. A James O'Connor try and Christian Lealiifano conversion reduced the deficit before Lealiifano kicked two penalties to make it 16-19.
But the Lions took control as tries from Sexton, George North and Jamie Roberts helped seal victory.
In total, player of the series Leigh Halfpenny chipped in with 21 points for the Lions.
Congratulations to the team, management and supporters on a memorable series triumph.
And a special word of congratulations to our six representatives; Cian Healy, Jamie Heaslip, Rob Kearney, Sean O'Brien, Brian O'Driscoll and Jonathan Sexton.