Dundee were denied a first home victory over Celtic for 37 years as Arne Engels' stoppage time penalty earned a 3-3 draw for the Scottish champions on Tuesday.
A topsy-turvy thriller saw the visitors twice lead at Dens Park through former Dundee captain Luke McCowan and Yang Hyun-jun.
But the home side rallied to level through Oluwaseun Adewumi and Cameron Carter-Vickers' own goal before Aaron Donnelly headed Dundee in front 12 minutes from time.
Substitute Engels converted from the spot after Mohamed Sylla's handball but Celtic dropped points for only the fourth time in the league this season.
Brendan Rodgers's men still enjoy a huge 16-point lead over Rangers, who host Aberdeen on Wednesday.
"It was a disappointing result from our perspective," said Rodgers.
"I give credit to the players, they kept going. But for our standard, that second half has to be better.
"Tonight was about doing the basics of the game well, and we did not do that well enough."
Dundee have now held both Celtic and Rangers at Dens Park in each of their last two games.
"We made a Champions League team wobble," said Dundee boss Tony Docherty.
"We sensed it, we went for it and gave everything to win that match. I thought my players deserved that tonight."
A point edges Dundee up to seventh and within two points of the top six.