They looked to be on their way to another three points when, after a tight start to the game, Coloccini gave them a 38th-minute lead when he latched on to Siem de Jong's corner and beat goalkeeper Brad Guzan.
To their credit, Villa, who arrived on Tyneside without a win in 15 league outings since the opening day of the campaign, refused to buckle and grew into the game as it wore on with substitute Rudy Gestede having been introduced to allow them to take a more direct approach.
That said, Newcastle should have wrapped up the win with 57 minutes gone when Georginio Wijnaldum picked out the unmarked De Jong and saw him head wastefully wide with the goal at his mercy.
Villa took full advantage of their escape within four minutes when midfielder Jordan Ayew capped an impressive individual display with a right-foot missile to level the scores.
Magpies keeper Rob Elliot made a fine late save from Gestede and substitute Ayoze Perez fired over at the other end as the game reached a tense conclusion, but ultimately both managers had to settle for a point.
Villa boss Remi Garde was delighted with the response of his players, and particularly Ayew's contribution to a game he will hope is a turning point for a club which will head into Christmas rooted to the foot of the table.
Garde said: "It was a brilliant goal from Jordan Ayew. He is a very talented player, but not only talented, he works hard for the team defensively, offensively and he has been rewarded by a very nice goal.
"It's good for his confidence, it's good for the confidence of the whole team. He has been helped by all his team-mates and of course I want to congratulate him for what he did, but as a manager I have to say as well that all the players worked hard in the second half and that's why we came back."