Trailing to strikes by James Forrest and Anthony Stokes, Hearts imploded and surrendered their 11-game unbeaten run.
Kenny Deuchar's header increased the home side's lead before Anthony Stokes pulled a goal back for Hibs.
Anthony Stokes opened the scoring from the penalty spot after Dons captain Paul Hartley saw red for handball.
Anthony Stokes had made his Celtic debut after arriving from Hibernian, replacing Georgios Samaras beside Murphy up front.
Anthony Stokes headed over the bar when he rose unchallenged to meet Maloney's cross in the 31st minute.
The visitors broke the deadlock when Anthony Stokes' low drive deflected in off the heel of hapless Garry Kenneth.
Anthony Stokes had perhaps been harshly penalised for a challenge on Aiden McGeady and a spot-kick was the result.
The latter player conceded a penalty in added time in the process, which Anthony Stokes scored to level the game.
Scott Brown and Mark Wilson were missing through suspension, while Daniel Majstorovic was injured and Anthony Stokes dropped to the bench.
Anthony Stokes was making his debut for Celtic since arriving from Hibernian and Lennon liked what he saw from the striker.
The hosts complained, but it mattered little in the end as John Rankin teed up Anthony Stokes to blaze over the crossbar.
Former Sunderland striker Anthony Stokes broke the deadlock in 41 minutes when he latched on to Derek Riordan's through ball and slotted home.
Home substitute Byrne, on for early injury victim Merouane Zemmama, did get a glimpse of goal after some impressive work from Anthony Stokes.
BBC: SPORT | Football | Scottish Premier | Hibernian 2-0 Aberdeen
Mensing also saw red for a foul in the box, Anthony Stokes converting from the spot before having a goal disallowed deep into injury time.
But Danny Collins and Anthony Stokes failed to find the target with flashing first-half headers and Kenwyne Jones could not turn in a left-wing cross.
Anthony Stokes, who had earlier had a goal disallowed for offside, levelled in the 63rd minute and both sides missed chances to grab a late winner.
And, eight minutes into the second half, Irish striker Anthony Stokes scored the first of his two goals on the night by curling a free-kick past the despairing Hearts goalkeeper.
However, this season's prize for the best goal has already been handed to Hibs' Anthony Stokes but Jutkiewicz was slightly more concerned with the importance of his strike than its flair.
Striker Steven Fletcher departed Hibs to join Burnley this week and Hughes has been linked with moves for Rangers' Alan Gow and Sunderland's Anthony Stokes, the forwards he worked with at Falkirk.
However, immediately after the break, Celtic handed Riordan the chance of an equaliser when Anthony Stokes, so recently a Hibs player himself, was short with a pass back, but the former Hoops forward was unable to capitalise.
Sunderland were still refusing to lie down, with substitute Anthony Stokes bringing a fine save from Almunia and Jones shooting across the face of goal with the Arsenal keeper out of position following a fine run by Miller.
Lukasz Zaluska returned to Celtic goal after Artur Boruc was left out due to a family bereavement, while John Hughes dropped Lewis Stevenson to the bench and Chris Hogg was left out altogether as Anthony Stokes and Darren McCormack came in.
应用推荐