However, despite Odsonne Edouard's goal in the 96th minute, the Northern Irishman was critical of the pace of his team's play.
Lennon chopped and changed personnel and system in the second half to inject a bit more verve into his side's play.
With Jonny Hayes working well down the left, it was a combination of Edouard and James Forrest who ultimately earned Celtic the three points at Dens Park.
"It's a brilliant win, it's a significant win and it's a very important win.," Lennon told Sky Sports. "It's what we deserved over the course of the game and we have to remember that Dundee are playing for their livelihoods and playing for their league standing and their not just going to lie down and roll over which they didn't do.
"We got a little bit bogged down for periods in game even though we had so much possession and we changed it, went to a back three to get more width at times. Hayes was starting to cause them problems.
"Our final ball, our final third entries wasn't great. We created some good chances in the first half, unlucky not to be one or two up but we could easily have been undone end of the first half.
"We kept going and we produced a bit of urgency and a bit of quality, a bit of speed to the attack which had been lacking all day and we scored a great goal.
"There's times I don't like the way we play without being over critical. I think we are a little bit slow and a little bit pedestrian at times and I would like to speed things up a little bit but I can't have everything. They've won the game and that's all I can ask of them at the minute."
Celtic now enter the international break with Rangers the next opponents when they come back, giving them an opportunity to extend their lead at the top further.
"It's huge," Lennon said when asked about the ten point gap. "We're not taking anything for granted but it is a very welcome cushion at the minute."