Didier Agathe scored a priceless first goal for Celtic in the dying seconds to give Neil Lennon a winning start to his Celtic career. After his £5.75 million arrival this week all eyes were on the midfielder, but it looked like he would have to settle for a point at Dens Park as Tom Boyd's own goal cancelled out Stilian Petrov's opener.
A draw would have been a fair result, but with time running out Agathe headed home at the far post to extend Celtic's lead at the top of the Scottish Premier League to seven points. Lennon, whose touches were greeted with cheers from the green and white faithful, made his presence felt from the first whistle and made a vital challenge on the edge of the box to thwart Claudio Caniggia as he shaped up to shoot.
But the former Crewe man was soon celebrating a goal in only the fourth minute when Bobby Petta fed the ball to Lubo Moravcik, who played the ball back into the path of Stilian Petrov, who slotted it home past Marco Roccati.
Dundee, however, should have taken the lead moments later when Joos Valgaeren failed to cut out a cross from Carranza. The ball fell to Juan Sara inside the box, but Petrov made a vital challenge. Lennon almost created Celtic's second on 28 minutes when he played Moravcik clean through on goal, but the Slovakian's first touch let him down and Roccati was able to make a telling block.
Celtic were struggling to come to terms with the pace of Caniggia and on the half hour they had Valgaeren to thank for keeping their lead intact. The Argentinian striker ran onto Carranza's pass and took it round Douglas, but the Belgian defender got back to clear off the line.
Douglas then had to be alert in the 35th minute when Marcello Marrocco's cross took a deflection goalward off Johan Mjallby, but the goalkeeper made a vital save on his line.
In the final seconds of the half Celtic should have done better when Moravcik fed the ball through to Thompson, who fired straight at Roccati.
Celtic could have extended their lead just three minutes into the second half when Petta's corner found Valgaeren at the near post, but the defender volleyed just past the upright.
But Dundee deservedly drew level in the 55th minute and it came fortuitously after Caniggia had put the Celtic defence on the back foot again. The striker crossed towards Sara in the box, but Celtic skipper Boyd, under pressure, intercepted and headed past his own keeper Douglas. Celtic's uncertainty at the back was again evident on the hour mark when Sara played the ball through to Caniggia, who rounded Douglas before firing into the side netting from a tight angle.
The home side thought they had taken the lead in the 73rd minute when Carranza picked out Caniggia with his free-kick, but Douglas pulled off a great save to his right to keep out the striker's header.
But nobody could forecast the drama at the end of the game as Celtic grabbed the points. Petrov's corner caused a huge goalmouth scramble and the ball appeared to strike Mjallby's arm before coming off Tweed and on to Agathe at the far post.
DUNDEE: Roccati, Smith, Tweed, de Marchi (C. Coyne 6), Marrocco, Artero (McSkimming 70), Rae, Nemsadze, Carranza (Milne 88), Sara, Caniggia. Subs Not Used: Langfield, Yates. Booked: Smith. Goals: Boyd 55 og.
CELTIC: Douglas, Valgaeren, Boyd, Mjallby, Agathe, Lennon, Petrov, Thompson, Petta (McNamara 64), Moravcik (Johnson 46), Larsson. Subs Not Used: Gould, Mahe, Healy. Booked: Boyd, Thompson. Goals: Petrov 4, Agathe 90. Att: 10,763.
Referee: John Underhill (Scotland).