The Hoops were served by a Kris Commons penalty on the stroke of half-time, which saw Dons keeper Jamie Langfield sent off, before James Forrest's deflected effort wrapped it up with three minutes remaining.
The win comes ahead of Tuesday night's first leg Champions League qualifier playoff against Kazakhstan's Shakhter Karagandy and Lennon was happy to head over there on the back of a positive performance.
"I'm delighted with the win," Lennon said. "It's been a difficult week because the boys have been away. We only had one day to prepare.
"We were a little bit slow starting again but we started to impose ourselves on the game and obviously got a break with the red card and the penalty.
"But I felt we were starting to get on top.
"It's definitely a confidence booster and we will be able to add four or five players to the squad. We are having Shakhter watched today so tomorrow we can have a good look and prepare as we possibly can."