Kelechi Iheanacho was Celtic's hero as he climbed off the bench to keep their Premiership title hopes alive with a late winner at Dundee.
Martin O'Neill knew his side needed all three points at Dens Park to remain in the chase and Hyun-Jun Yang sent them on their way with an early opener.
They should have extended their lead with Tomas Cvancara missing two brilliant chances before Simon Murray pulled the hosts level after Colby Donovan's handball.
Iheanacho replaced the on-loan forward and sparked wild celebrations when he sent Marcelo Saracchi's cross into the net.
"He's a very fine player," said Celtic interim boss Martin O'Neill after the game. "At 29 he should be at the peak of his career rather than scratching around. He has played for Manchester City.
"That will do him the world of good. He's absolutely buzzing in the dressing room."
Dundee, who beat the Hoops at home earlier this season, were dealt a second blow with Ryan Astley sent off for a late challenge on Yang.
The win moves Celtic to within three points of Hearts after their draw at Livingston. Rangers remain in second, one point off the summit.
Celtic had lost three times in Tayside this season with three different managers in charge, but the defending champions ended their hoodoo to remain in the hunt.
Yang opened the scoring after eight minutes by getting a slight touch on Benjamin Nygren's close-range shot and they should have been further in front before half-time, with Cvancara wasteful in front of goal.
And that wastefulness came back to bite them after the break.
Video assistant referee (VAR) Matthew MacDermid spotted a handball by full-back Colby Donovan and referee Steven McLean pointed to the spot after going to the pitchside monitor.
Home captain Murray calmly converted to level the score and Celtic took their time to wrestle back their momentum.
However, with time running out, substitute Iheanacho lashed a left-footed shot past goalkeeper Jon McCracken to secure all three points.
Dundee were then reduced to 10 men as centre-back Ryan Astley was dismissed for taking out Yang.
Celtic boss Martin O'Neill speaking to Your Site:
"We should have been out of sight in the first half.
"We missed quite a number of chances. I always felt it might just come back to haunt us, really. Dundee having the advantage of the wind in the second half, down whatever particular slope it is as well.
"But for us, conceding the penalty, we could have just keeled in and said, 'well, that's not going to be our day'. We fought back. It was great for us to win the game.
"It keeps us there, we're still fighting on.
"For us to win today, that was a really big success and it keeps us in it.
"Naturally, I'm just delighted for the crowd. The crowd were magnificent the whole afternoon. Kept us going in all honesty.
"Six games to go, three points between the top three."
The title race is too close to call for Your Site pundit James McFadden:
"You're looking at Hearts, expecting them to win comfortably at Livingston. They're in a great position, they get pegged back and draw the game.
"Rangers, people expect them to win at Ibrox. Celtic, you weren't sure whether you were going to get a performance or purely a result. You got the result and there were good elements of the performance, there's still things to improve upon.
"It just shows you that you still don't know. You could make a prediction every week and get it wrong."
