Despite dominating possession it took the Hoops until the 32nd minute to break down bottom of the the table Dunfermline's defence when Charlie Mulgrew sent a wonder strike beyond Chris Smith from 30 yards.
The Pars keeper then kept Celtic at bay until the 75th minute when substitute James Forrest slid in a second as the Hoops won their 16th league match in a row - a run that extends back to November.
It keeps Celtic on course for a domestic treble while Old Firm rivals Rangers, who were docked 10 points after entering administration last week, continue to fight for their financial survival.
Motherwell, who are the visitors to Parkhead on Saturday, closed the gap on Rangers in second place to just three points after defeating Hibernian 4-3 at Fir Park.
In Glasgow, Celtic manager Neil Lennon was afforded the luxury of making four changes to the side who thrashed Hibernian at the weekend.
The home side dominated early possession with Ki Sung-Yeung's strike from long range forcing a save from Smith after the ball bobbled in front of him before Anthony Stokes came close with a dipping shot.
Gary Hooper should have put the Hoops in front after 18 minutes when he was sent one-on-one with Smith by Cha Du Ri's pass but the keeper made a vital save to turn his effort round the post.
Smith was equal to a curling strike from Stokes minutes later but could do nothing to stop Mulgrew giving Celtic a 32nd minute lead with a superb shot.
The ball broke to the defender just inside Dunfermline's half and Mulgrew took a touch before letting fly with a vicious strike that crashed into the top right hand corner of the net.
Moments later Hooper's cutback found Kris Commons with room in the box but his low shot was dealt with by Smith.
Alex Keddie sent his header straight at Fraser Forster as he connected with Joe Cardle's corner in a rare foray forward by Dunfermline.
Stokes should have doubled Celtic's advantage four minutes after the break when Emilio Izaguirre picked him out unmarked at the back post with his cross but the Irish striker sent his shot past the post with the whole goal to aim at.
The chances kept coming for Celtic and when Smith could only parry Joe Ledley's shot as far as Hooper a second goal looked inevitable, but the striker hooked his shot high over the bar.
It looked to be a case of damage limitation for Dunfermline but they could have sneaked an equaliser in the 60th minute when Ryan Thomson's effort from a Paul Willis corner was headed off the line by Izaguirre.
That represented rare respite for the Pars defence and Smith again came to the rescue when he tipped a controlled volley from Scott Brown over the bar from Ki's cutback.
Celtic got the second goal their pressure deserved in the 75th minute when Hooper's cross from the by-line evaded everyone apart from substitute Forrest, who slid in at the back post to knock it past Smith.
Source: AFP
Source: AFP