Many expected the floodgates to open after Kris Commons netted the opener after just 12 seconds, but the valiant Dons bounced back and opened up a 3-1 lead.
However, Charlie Mulgrew pulled one back and Gary Hooper equalised with three minutes remaining before substitute Georgios Samaras fired the winner in added time to settle a thrilling contest.
"It was absolutely brilliant," said Lennon. "People were accusing the players or criticising the players for complacency and not showing enough desire.
"But when the fourth goal went in I think you could see what it meant to them and what it meant to the supporters. It was like the good old days.
"I know we have got a few defensive problems that we need to sort out. We keep giving cheap goals away but our desire to win the game was fantastic.
"I have been waiting on this team to do that for a wee while and they showed me that today."
Match-winner Samaras added: "It was a great goal for the team. We showed great character to come back, it is something special so well done to all the boys.
"Sometimes we play bad and lose, sometimes we play bad and win, but nothing can compare with this game."