Anthony Stokes looked to have put the Hoops on course for a 21st consecutive win in domestic competitions when he rounded Jason Brown and slotted the ball home from an acute angle after 28 minutes.
Celtic had not conceded in their previous six matches, but Aberdeen equalised when Gavin Rae's shot took a wicked deflection off Celtic debutant Andre Blackman and flew
past Fraser Forster a minute before the break.
A spirited second-half display from Aberdeen helped them continue their own unbeaten run, which now stretches to 12 games.
Defenders Mikael Lustig and Blackman were both handed first starts for Celtic as the visitors made four changes with Kris Commons and Stokes also included in the starting XI.
Manager Neil Lennon had to do without the services of Ki Sung-yueng and Emilio Izaguirre, who had both failed to return in time from international duty, while Swedish defender Daniel Majstorovic was absent after suffering cruciate ligament damage.
The Dons made only one change from the team which drew 1-1 with St Mirren last weekend, with New Zealander Rory Fallon stepping in to replace Youl Mawene, who dropped to the bench.
Celtic had the first chance of a frantic opening period when Rory McArdle upended James Forrest on the edge of the area and Charlie Mulgrew, who earned his first Scotland cap against Slovenia in midweek, hit the woodwork with a well-struck free-kick.
The hosts carved out their first opening after 11 minutes when Rae found Fallon at the back post, but his header drifted wide as the flag went up for offside in any case.
The visitors opened the scoring after 28 minutes when Mulgrew, who was enjoying a rare outing in the centre of midfield, threaded the ball to Commons who in turn fed Stokes to round Brown before turning the ball home from an acute angle.
Aberdeen had Brown to thank 10 minutes later when he had to be alert to keep out Stokes' low free-kick after Blackman had been fouled on the edge of the box.
The Dons were desperately trying to find a route back into the game and the equaliser came a minute before the break when Scott Vernon fed Rae, whose left-foot shot took a wicked deflection off Blackman to leave Forster with no chance.
Aberdeen made a bright start to the second period when Ryan Jack played an inviting cross into the box for the unmarked Fallon, but the striker was unable to connect.
Tempers began to flare when Aberdeen opted not to give the visitors the ball back after Hooper had received treatment for a head knock, before Stokes was fortunate to avoid punishment for catching Jack with a late challenge.
Celtic made their first switch after 59 minutes when Blackman's first appearance came to a premature end and Victor Wanyama was introduced.
The home side should have taken the lead after four minutes later when Rae played in Mitch Megginson, but the youngster dragged his shot wide.
Celtic brought on Dylan McGeouch and Cha Du-ri for Lustig and Commons as they pushed for a second, while Aberdeen were forced to bring on Peter Pawlett after Fraser Fyvie limped off with an injury.
Dons goalkeeper Brown was equal to Stokes' drilled effort and easily held a Hooper header as Lennon's side looked to preserve their winning run.
But the Dons held firm in the closing stages to take a well-earned point and end Celtic's winning run which had stretched back to October.
