Earlier, Ki Sung-yong had put the home side ahead before Ryan Jack, who later saw red for a second bookable offence, leveled on the hour-mark.
Lennon was delighted with the showing of his side, especially Mulgrew who has been in a rich vein of form this week.
"Charlie scored with his right foot so he has had a good week," Lennon said.
"He scored last week and set the goal up in midweek and scored again today.
"He has been really consistent for us this season and I am delighted for him - I think it is the first time he has captained a winning Celtic team.
"He made a mistake last week and corrected it with the third goal.
"He has played brilliantly for the majority of the season and came up for the winner today.
"His improvement since he came back here has been huge.
"It is a credit to him that he went away down south to forge his career and didn't give up on it and now he is captaining Celtic which is a great achievement for him."