With Kilmarnock on cup duty and Dundee United not playing, the Dons took full advantage to move above the pair and into the top half of the table for the first time in Craig Brown's tenure.
Dons striker Vernon took full advantage when Iain Turner raced from his line to try to collect Mark Reynolds' searching pass, headed the ball over the stranded goalkeeper to score the only goal of the game after 24 minutes.
Aberdeen's new signing Stephen Hughes started on the bench as the Dons made only one change from the side that drew 1-1 against Rangers at Ibrox last weekend with skipper Andrew Considine returning from a hamstring injury to replace New Zealand striker Rory Fallon.
Dunfermline included former Dons captain Mark Kerr in their starting XI and made two changes from the team that lost 3-1 to Motherwell on Tuesday.
Paul Willis and Ryan Thomson both started with striker Andrew Barrowman missing out after pulling a calf muscle in the loss to the Steelmen and Joe Cardle dropping to the bench.
Last time the sides met at Pittodrie, the Pars were on the wrong end of a 4-0 trouncing but they made a positive start to this encounter with Kerr picking out Liam Buchanan whose deflected shot drifted wide for a fruitless corner.
The hosts carved out their first real opening after six minutes when Rory McArdle crossed for Fraser Fyvie but Turner managed to tip the midfielder's low shot past the post.
Dunfermline should have broken the deadlock after 13 minutes when David Graham's perfect cross picked out the unmarked Buchanan but the striker's header was straight at Jason Brown in the Aberdeen goal.
The Dons almost capitalised when Turner flapped at a Fyvie cross after 20 minutes but Reynolds' header just cleared the crossbar.
Aberdeen made the breakthrough after 24 minutes when Reynolds picked out Vernon with a hopeful pass upfield and the Englishman's first-time header looped over the badly positioned Turner and into the unguarded net.
The Dunfermline goalkeeper went some way to making amends for his error by managing to keep out a Chris Clark drive, which took a wicked deflection, with his leg just before the break.
The Dons looked eager to put the result beyond doubt in the early stages of the second half with Clark Robertson firing well over and Vernon outpacing Kevin Rutkiewicz but his angled shot was well handled by Turner.
The hosts wasted another opportunity on the hour mark when they were awarded a free-kick in an inviting position but Turner was equal to Kari Arnason's weak, low drive.
However Dunfermline were enjoying large chunks of possession with Graham proving a particular nuisance to the Dons rearguard.
In a bid to stem the Pars' attacks, the home side introduced Hughes for his debut and Mohamed Chalali for Magennis and Fyvie after 69 minutes.
The Pars introduced Andy Kirk and Cardle for Willis and Buchanan with 11 minutes remaining as Jim McIntyre's side pressed for the equaliser.
And it was Cardle who should have earned his side a point two minutes from time when he latched onto McArdle's slack backpass but Brown denied the Dunfermline substitute to ensure the Dons held out for the win.