Amid a night of missed chances, defender Charlie Mulgrew celebrated his first Scotland call-up with a wonderful strike in the first half before substitute James Forrest, on for Emilio Izaguirre, made it number two after the break from close range.
The Hoops extended their domestic winning run to 19 games and 13 in all competitions, equalling a feat achieved by Martin O'Neill's side in 2004, in which Lennon was a lynchpin. However, the Celtic boss revealed he keeps reminding the Hoops class of 2012: "Don't spoil it. Don't let the run get away."
He added: "Something like this happens maybe once in your career and they should be proud of it and try to hold on to it as long as they can, that's all I am asking them to do.
"We could easily have switched off and they could have gone home thinking they had chucked it away but they didn't and I am delighted.
"I thought we made it hard for ourselves. The only criticism I can level at the players is that they were wasteful in front of goal.
"Apart from that I'm very proud of the team and the way they are playing, They have opened up a huge gap in the championship and I couldn't ask any more."
Dunfermline remain at the bottom of the table fighting for their SPL status with Hibernian.
But manager Jim McIntyre praised much-maligned keeper Chris Smith for keeping Celtic at bay for most of the game.
"He showed great character," said the Pars boss. "He has made a couple of mistakes this season and he has been vilified in the press but what you have to say is that he responded in the right manner. I thought he had an outstanding game."
Source: PA
Source: PA