Lyle Taylor turned in Callum Kennedy's cross for his 23rd goal of the season.
And substitute Adebayo Akinfenwa netted a penalty in the 11th minute of injury time after a foul on Adebayo Azeez.
The Dons achieved a sixth promotion since their formation in 2002 by fans of the old Wimbledon FC following their relocation to Milton Keynes.
Argyle, who topped the Championship back in August 2004, will remain in League Two for a sixth season, having almost gone bust in 2011.
Promotion for AFC Wimbledon keeps the remarkable story of the club's rise from the aftermath of Wimbledon's move to Milton Keynes going.
They have now won six promotions since they first took to the field in the Combined Counties League in the ninth tier of English football.
While the club still hope to return to their home borough of Merton, next season raises the tantalising prospect of two league fixtures with MK Dons, who were relegated from the Championship.
The clubs have played three times before in cup matches - all at Milton Keynes - with AFC Wimbledon getting the better of MK Dons once.