A late goal from Henrik Larsson was enough to maintain Martin O'Neill's 100% record as Celtic manager and reclaim the team's place at the top of the Scottish Premier League table.
Dunfermline looked like holding on for the draw after an explosive two-minute period in the second half.
Chris Sutton was judged to have handled in the area and Steve Crawford converted from the spot to give Pars the lead.
But just one minute later Larsson levelled from the spot after Justin Skinner brought down Paul Lambert.
And Larsson's cool clincher four minutes from time capped the comeback for O'Neill's men at East End Park.
Dunfermline had also enjoyed a great start to their league campaign but it took Jackie McNamara just four minutes to break down the Pars' defence when he pin-pointed Larsson in the box but the Swede failed to connect properly and nodded the ball wide.
Alan Thompson settled into the Celtic side quickly and burst into the box four minutes later - but his shot from a tight angle smacked off the near post.
For the opening period of the game Celtic enjoyed the best of the goal-scoring opportunities and on 20 minutes Paul Lambert came close when he rifled a shot wide from 20 yards.
Just seconds later team-mate Thompson became the first player of the night to find himself in referee Willie Young's for a nasty challenge on Rob Matthaei.
Undeterred Matthaei almost set up Dunfermline's opener just four minutes later when he sent a great pass through to Lee Bullen who was running in on goal, but he was blocked by the vigilant Swede, Johan Mjallby.
Ten minutes before the break Chris Sutton almost found the net for Celtic when he met a Larsson cross but blasted the ball wide of the mark.
On 41 minutes the pressure seemed to be getting to former Rangers star Ian Ferguson, who was booked for a challenge on McNamara.
The game erupted after the interval when Joos Valgaeren was booked for a challenge on Matthaei on 56 minutes. Minutes later Stilian Petrov was booked for diving.
And just two minutes later Sutton joined his team-mates when he was ruled to have handled the ball in the area.
Goalkeeper Jonathan Gould was also cautioned for dissent but Crawford coolly stepped up to slot home the spot-kick.
But Dunfermline's lead was short-lived when Justin Skinner brought down Lambert inside the box and Larsson stepped up to send the keeper the wrong way from the spot.
Celtic were desperate for the second and pushed everyone forward in the last 10 minutes, but were finding it difficult to break down the Dunfermline defence.
But Larsson struck just four minutes from time with the clincher when he met a Sutton pass and skipped around the goalkeeper, before slotting in from close range.
In the dying seconds of the game Sutton almost added the third, but again the former Chelsea man sent the ball wide.