The Bairns, inspired by a flawless display from veteran midfielder Neil McCann, won the tie thanks to an early second-half strike from Tam Scobbie and an 89th-minute penalty by Scott Arfield to ensure their first appearance in the final of the tournament since 1997.
It was clear from the start that Falkirk intended to take the game to Dunfermline and they posted early notice of their intentions when striker Michael Higdon swivelled on the edge of the penalty area before firing in a shot which clipped the outside of Paul Gallacher's right-hand post.
Arfield then tested Gallacher with a crisply struck 25 yarder and the young midfielder also forced a save from the Pars keeper with an ambitious headed effort.
McCann, Arnau Riera and Carl Finnigan all came close to opening the scoring as Falkirk dominated but Dunfermline, for whom the overworked Gallacher was in excellent from, held out until the welcome respite of the half-time whistle.
The second half began in familiar manner with Falkirk on top and they took the lead just nine minutes after the interval when young defender Scobbie outjumped the Pars defence to meet a superbly floated free-kick from McCann with a forceful close-range header which flew beyond the stranded Gallacher.
Motivated by Scobbie's opener, Falkirk pressed for a second goal and it almost arrived when McCann made space for himself in the penalty area before shooting high over the bar from 15 yards out.
The Fifers finally managed an effort on target in the 65th minute when a well-struck shot from Jamie Mole was held by the diving Dani Mallo in the Falkirk goal.
With time running out, Dunfermline substitute Greg Ross downed man-of-the-match McCann in the penalty area and, from the resultant spot-kick award, Arfield sent Gallacher the wrong was to make sure of victory, a return trip to the National Stadium next month and, for the first time in the club's history, a place in European competition.