A late goal from Henrik Larsson was enough to maintain Martin O'Neill's 100 per cent 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 the 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 pinpointed Larsson in the box but the Swede failed to connect properly. For the opening period of the game Celtic enjoyed the best of the goal-scoring opportunities. 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.
DUNFERMLINE: Ruitenbeek, Nicholson, Skerla, Skinner, Doesburg, Matthaei (Boyle 88), Ferguson, S Thomson, Bullen, Crawford, Mendes (Dair 71). Subs Not Used: Reid, S Thomson, McGarty. Booked: Ferguson. Goals: Crawford 60 pen.
CELTIC: Gould, McNamara, Valgaeren, Boyd, Mahe (Moravcik 67), Petrov, Mjallby, Lambert, Thompson, Sutton, Larsson. Subs Not Used: Stubbs, Kerr, Burchill, Riseth. Booked: Thompson, Valgaeren, Petrov, Gould, Sutton. Goals: Larsson 62 pen, 85.
Referee: W Young (Scotland).