Gary Hooper had opened the scoring just before half time shortly after Rab Douglas had saved a Scott Brown penalty.
The former Celtic keeper had an inspired afternoon against his old side with the woodwork coming to his rescue a couple of times.
Tunisian striker Lassad Nouioui started his first match since signing on transfer deadline day with Efe Ambrose making a late appearance as a substitute.
Teenager Tony Watt made a big impact on the game against a tiring Dundee defence with Lennon admitting that he is concerned by the low rate of chances being converted.
“What isn’t a concern is the chances that we are creating,” the Celtic boss explained. “We are doing that on numerous occasions in games – but I would like to see us start putting a few more away.
“We lacked a little quality at times in the final third but the build-up play was pretty good and defensively we looked pretty comfortable all afternoon. It was a good performance, a clean sheet and three points which is what I wanted.
“There was a good tempo to the game. We had to wait a wee while for the breakthrough but it was a quality goal from Gary after really good play between him and Scott.
“We got a great second goal in the second-half and I felt after that it was one-way traffic and the only disappointment was we didn’t get more goals.”
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