Close-season signing Michael Moffat had a couple of opportunities in the first half but was denied firstly by defender Paul McLean and then by Graeme Smith.
Smith was the busier goalkeeper in the opening 45 minutes but Dunfermline could not find a way through. Brechin were better after the break and Ryan Scully had to react smartly to deny Robert Thomson from Colin Hamilton's cross.
As Dunfermline responded, Smith did well to get his hand to a Ross Forbes free-kick which was bound for the top corner and then captain Andy Geggan was not far away with a volley that flew past a post.
Dunfermline seemed to run out of ideas as the match wore on against a well-organised Brechin side and were almost punished when Thomson hit the post.
Ayr United did just enough to see off 10-man Morton 1-0 at Somerset Park, the only goal coming from new signing Ryan Donnelly with 11 minutes remaining.
The match was pretty even until the visitors had Jordan Allan sent off midway through the second half for a wild lunge on Alan Forrest.
Peter McGill forced a good save from Derek Gaston as Ayr sought to kill the game but Morton had chances to salvage something, notably through Declan McManus who shot over in injury-time.
Stenhousemuir were the only other team to open with a win, but they left it late to edge out Airdrieonians 1-0 at Ochilview.
Airdrie had looked the more likely to score with Jim Lister going close on a couple of occasions in the first half.
Lister also troubled the home side in the second half but Stenhousemuir held it together at the back and were rewarded when Martin Grehan struck the winning goal with three minutes to play.
Rory McAllister rescued Peterhead with a late strike in their 1-1 home draw with Stirling Albion.
After a goalless first half, McAllister almost broke the deadlock just after the break with a lob which dipped just over.
Bryan Gilfillan forced a decent save from Greg Paterson, but Gordon Smith put Stirling ahead when he kept his cool to net after Louis Coult had created the opening. McAllister equalised five minutes from time to earn his side a point.
It was also honours even at Stair Park as Stranraer and Forfar Athletic played out a 1-1 draw.
The hosts' Jamie Longworth did not take long to score his first league goal of the season, netting after 17 minutes. However, Forfar hit back with Stuart Malcolm equalising after 64 minutes.