With his Dundee squad already down to the bare minimum, boss Jim Duffy was forced to use the same defenders that conceded five goals at Motherwell in midweek.
The visitors started on top and captain Scott Thomson saw two shots from outside the box saved by Julian Speroni in the Dundee goal inside the first quarter of an hour.
With 19 minutes played, Noel Hunt got on the end of a deflected cross and almost beat Speroni with a looping header but the keeper did well to gather.
Andrius Skerla headed just over from eight yards out on the half-hour mark.
It seemed only a matter of time until the visitors took one of their chances and with 32 minutes played they finally moved into a deserved lead.
The Dundee defence failed to clear a Greg Shields cross from the right and when the ball broke to Hunt he bundled the ball over the line from close range.
The one-way traffic continued after the break and Dundee keeper Speroni denied Richie Byrne on 52 minutes when he saved his header from Barry Nicholson's corner.
With just over an hour played Dundee substitute Mark Fotheringham went close when he hit a powerful right-foot effort inches over the crossbar from 25 yards.
Dundee went even closer on 65 minutes when defender Lee Mair headed Fotheringham's corner goalwards but to his dismay defender Darren Young cleared off the goal-line.
With 12 minutes left only a great save from Derek Stillie low to his right denied Nacho Novo an equaliser after a neat one-two with Fotheringham.
Duffy took a gamble with 12 minutes remaining when he replaced defender Tom Hutchinson with young striker Steven Robb and moved to a four-pronged attack.
However, it wasn't to be, and Dundee rarely troubled Dunfermline after that as the visitors collected a deserved three points.