Celtic remain unbeaten domestically in two spells under interim manager Martin O'Neill this season, but may feel they wasted an opportunity to reel in leaders Hearts.
The Jambos are aiming to end a 40-year grip on Scottish football by Old Firm giants Celtic and Rangers.
They maintain a six-point cushion over Celtic, who have won 14 of the last 15 Scottish Premiership titles.
The defending champions made the perfect start when Benjamin Nygren's free-kick arrowed into the top corner.
Hearts were without a number of key players due to injury, but battled back in the second period as Stuart Findlay headed in from a corner.
Yang Hyun-jun restored Celtic's lead after an impressive run and cross by debutant Tomas Cvancara.
But for the second time in four days, O'Neill's men failed to hold onto a lead after being reduced to 10 men.
Reo Hatate saw a first-half red card in a 2-2 Europa League draw at Bologna on Thursday.
This time, Austin Trusty was sent off after a VAR review for denying a goalscoring opportunity.
The visitors resisted until three minutes from time when Claudio Braga hammered in an equaliser.
Rangers closed to within four points of Hearts and edged ahead of their Glasgow rivals thanks to an eighth consecutive victory.
Danny Rohl's men had to wait until after half-time for the breakthrough at Ibrox through James Tavernier's penalty.
Two more goals in stoppage time from Danilo and Djeidi Gassama added gloss to the scoreline.