Barry Nicholson's 28th minute opener and a long-range strike from Gary Dempsey on 57 earned Dunfermline their first win at Celtic Park since they won by the same score there on August 16, 1997.
Henrik Larsson played his first home game for Celtic in that match but the Swedish striker's 47th minute header, his 238th goal for the Glasgow side, was not enough to salvage a draw as he prepares to depart at the end of the season.
"We've not played well today but it's about what you do over the season and we've won the title in 32 games," said Celtic manager Martin O'Neill, whose side were presented with their 39th championship trophy at the end of the match.
"The players are disappointed at losing today but they've been fantastic for us."
Dunfermline became only the third team to win at Celtic Park since August 2001.
Only Ajax Amsterdam and Aberdeen last month have defeated O'Neill's side -- whose domestic dominance is highlighted by nine league defeats in four years -- on their home ground.
"We'll now try and win the Scottish Cup while we are back in the Champions League and we'd like to push on from here next season," added the Northern Irishman, whose side were consigned to a trophy-less season in losing the title by a single goal difference to Rangers on the final day last term.
"They have come roaring back after the disappointment of losing it last season," O'Neill told reporters.
Celtic never found their best form against Dunfermline though the visitors still relied on an element of luck and some inspired goalkeeping by Derek Stillie to collect an unexpected three points.
In the first half they were content to soak up pressure but their counter-attacking strategy worked perfectly when they took the lead with the only meaningful attack of a dour first period.
The home side piled on the pressure afterwards but could not find a way past Stillie as he produced excellent stops from Johan Mjallby, Craig Beattie and Stanislav Varga while Chris Sutton also hit a post.
Celtic remain 13 points clear of Rangers before the final Glasgow "Old Firm" derby of the season on Saturday.
Dunfermline's win will give them confidence before they meet Celtic again in the Cup final on May 22.
