A 18th goal of the season Odsonne Edouard gave the points to Celtic
Odsonne Edward scored in the 96th minute with 10 points ahead of the Scottish Prime Minister. Dundee's reluctance fears grew worse.
James Forrest and Scott Sinclair worked hard as visitors dominated Dens Park.
Scott Wright could have put Dundee ahead, the midfielder scored on goal, but Scott Bain refused.
It seemed that the hosts had done enough to gain a point until Forrest was converted from his hand to Edward.
While the Rangers are in the draw on Saturday, Celtic increases its lead and could even extend it further when hosting the Ibrox team after the international break.
Dundee remains one point above the back of St Mirren, but the Buddies could overtake Jim McIntyre's team by winning their match against St Johnstone, five points ahead of Hamilton Academical in front of Dens Park. .
Celtic make pressure count – finally
The pressure of the Celtic was almost implacable. Kieran Tierney's efforts were deflected by a deep deviation, Forrest reversing a promising position and Callum McGregor unframed then countered by Seny Dieng. Tierney and Forrest would also close after the break.
The goalkeeper was less convincing with a lockout of Scott Brown's long ranger, giving Edward another chance to manage.
Dundee's hearts were back in the mouth when Celtic attempted a rehearsal repeat in the corners. McGregor found Forrest on the edge of the field and the volley of the Scottish winger was blocked by his teammate Brown just in front of goal.
Dieng's goalkeepers were more assured when Sinclair tried to get home on the left side of the pitch, with the Swiss getting a strong hand on the ball to return it. A similar Sinclair effort in the second half was thoroughly deflected.
The hosts had a hard time getting out their half but they missed the best opportunity of the first period. Kenny Miller released Wright but the striker traded the ball and Bain came out of his line to deflect the final shot.
Wright could not take the best of Bath
After the break, Celtic lost no time in terms of possession and territory, but chances were more rare.
The six minutes of overtime provoked local fans, who felt that there had not been so much playtime.
Dundee had been valiantly defended and had sought to counter where it was possible, but it was thanks to such a lead that they were defeated. Martin Woods' deflected shot was recovered by Bain and a few seconds later Celtic found the other end, Edward playing for Forrest twice and tapping at home in a six-yard congested area to send the fans home. the house delighted.
Frustration avoided for leaders – analysis
Celtic was looking for a missed opportunity for the second consecutive weekend before Odsonne Edouard's last goal.
Aberdeen held them at their home last Saturday after the Rangers tied with Hibernian the night before.
But the late goals in a crucial phase of the season made the difference for league leaders. Edouard scored his goal in the first game of Neil Lennon at the head of the Hearts club last month, while one of Brendan Rodgers' last games as Celtic boss featured a Scott Brown winner against Kilmarnock.
With eight league games to play and a semifinal of the Scotland Cup against Aberdeen next month, the winner of the League Cup, Celtic's bid for a third consecutive national treble, remains on the right track.