Former Hearts defender McCann netted his first goal for the Pars following more than 100 appearances after three minutes.
And Hibs were unable to beat an inspired Paul Gallacher in Dunfermline's goal as their struggles in Leith continued.
Hibs recorded three home wins in February, but have one win at Easter Road since - the September 28 defeat of St Johnstone.
It was Dunfermline's third win of the season - all of which have come away from East End Park - and first since August.
For all Hibs' attacking options - again Garry O'Connor was joined by Leigh Griffiths and Junior Agogo in an attacking line-up, with Ivan Sproule and Akpo Sodje in reserve - they looked blunt, with the quality of supply a growing concern.
The Pars, meanwhile, were workmanlike and worthy of victory through the one moment of quality in an otherwise dour game.
Hibs were seeking to continue a mini-revival after the win at St Mirren and goalless draw at Celtic - either side of the Scottish Communities League Cup loss to the Bhoys - and manager Colin Calderwood retained the same XI which began the match at Parkhead.
Striker O'Connor shot straight at Gallacher in the second minute, but moments later the hosts were trailing, with their defensive fragility exposed all too easily.
A Paul Willis cross from the right was converted at close range by McCann, who had made a run from deep.
The Pars had only scored first in three prior SPL games this season, winning two of them, and were looking to improve their record.
Hibs attempted to respond, but the final ball continually let them down.
The visitors were playing on the counter attack and Andy Kirk's attempted chip went over after 25 minutes.
Dunfermline slowly claimed more possession, but both teams were struggling to string together any meaningful passage of play.
The Pars went close after 36 minutes after Ryan Thomson's knockdown found Kirk, whose drive deflected narrowly wide of the post.
From the resulting corner Andy Dowie headed over and his complaint of being impeded in challenging for the ball was dismissed.
Danny Galbraith fired a 30-yard free-kick wide as Hibs again failed to test Gallacher.
Gallacher saved from Griffiths after David Wotherspoon's attempted cross and O'Connor's bid to follow up was blocked as Hibs missed the chance to draw level at the interval.
The hosts resumed on the attack, but John Potter and his defensive colleagues repelled the attempted crosses into Dunfermline's box.
A Wotherspoon cross was met by Griffiths, whose looping header was tipped over by Gallacher before O'Connor mis-cued a shot after the on-loan Wolves striker's cut back.
Griffiths missed a glorious opportunity after turning inside the edge of the area following Paul Hanlon's pass, the striker dragging his shot wide with only Gallacher to beat.
After Agogo was replaced by Sproule, David Stephens did well to block Liam Buchanan's run into the box.
Hanlon became the first player booked for persistent fouling before Gallacher turned O'Connor's header from Wotherspoon's cross over the bar.
Richie Towell came on for Lewis Stevenson as Hibs looked for a fresh creative spark and with 11 minutes remaining Sodje was introduced for O'Connor. But Hibs' troubles continued.
Wotherspoon had an effort saved by Gallacher before blasting the follow up over.
Galbraith shot well wide before Gallacher turned a Griffiths shot around the post in the first of four minutes of stoppage time.
Goalkeeper Graham Stack came up for the resulting corner, which was over-hit and the Pars prevailed as Hibs left the field to jeers from the home crowd.