A Kris Commons penalty and a deflected late strike from James Forrest gave the Hoops the three points against the Dons, who had goalkeeper Jamie Langfield sent off when conceding the spot-kick on the stroke of half-time.
"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. We made a little change with Charlie (Mulgrew) and Efe (Ambrose), swapping them around, because we were getting a lot of ball in midfield and we felt Charlie might manipulate it a bit more and dictate the play. That definitely worked in our favour.
"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."
Lennon expects forwards Anthony Stokes and Amido Balde to be fit for the play-off first-leg against Shakhter Karagandy on Tuesday, and Tom Rogic and Derk Boerrigter also travelled with the squad as they left for Kazakhstan via Aberdeen Airport immediately after the game.
Lennon does, however, have a slight concern over Adam Matthews who was feeling his hamstring as he left Pittodrie.