Seb Brown was the hero with two penalty saves after a goalless 120 minutes.
The success represents a remarkable climb up England’s football ladder for the Dons, who were only founded in 2002 as a direct result of Wimbledon FC’s relocation to Milton Keynes and subsequent transformation to MK Dons.
Just one division will separate those two sides next season, with AFC Wimbledon heading for League Two after an entertaining goalless encounter in front of 18,195 supporters at Eastlands.
Brown saved penalties from Alex Lawless and Jason Walker, leaving Dons skipper Danny Kedwell to fire home the penalty that clinched victory.
Luton striker Walker had headed against a post in the 89th minute before Dons counterpart Kaid Mohamed stroked a shot against the woodwork in extra-time.
Managers Terry Brown and Gary Brabin named unchanged starting line-ups from both legs of their respective semi-final triumphs.
And it was Dons boss Brown who was celebrating after eight minutes – only to see Kedwell ruled offside as he converted after Mark Tyler could only parry Mohamed’s effort from the left.
Kedwell saw his effort cause panic in the Hatters rearguard before Claude Gnakpa forced Brown into action at the other end.
The opening 45 minutes was a flowing affair, yet ill-discipline – which reared its head towards the end of the first half – was dominating over goalscoring opportunities as the clash approached the final half an hour of normal time.
Luton went closest to winning within 90 minutes when Walker saw his superb header hit a post and fall into the hands of Brown, shortly after AFC Wimbledon had survived an almighty goalmouth scramble.
Both sides started to show signs of tiredness in extra-time, while Mohamed almost snatched it in the 111th minute when he sent a great chance against a post.
It was left for Brown to produce heroics in the resulting shoot-out as AFC Wimbledon became the first club formed this century to join the Football League ranks.