East Fife 1 Dumbarton 0
They threatened early when Jason Dair, making his debut after spending time in the SPL with Livingston last season, linked with Ryan Blackadder before Paul Ritchie headed wide.
John Dodds' hesitation should have cost the Fifers on 26 minutes but Stephen Dobbie couldn't convert from close range.
East Fife took the lead on 39 minutes when John Martin's header was stopped on the line and Jablonski had two more efforts blocked before he finally found the net.
The Sons almost hit straight back but Dodds made a fantastic one-handed save from David McNaught's downward header.
McNaught should have levelled on 55 minutes when he outpaced the defence but Dodds made another fine block.
Dumbarton turned the screw and Dobbie forced the keeper into another save after winning a header in the box.
Substitute Chris Hamilton then broke the offside trap but his 71st minute effort was too weak to trouble the keeper.
Blackadder could have eased Fife nerves when he beat two defenders but he blasted his drive past the post.