The I-League champions, who beat Lebanese powerhouse Al Ansar in their opening pool match, wasted a couple of clear chances and conceded an own goal by Climax Lawrence.
Sur took the lead thro-ugh Daouda Traore in the eighth minute but Dempo levelled through Nigerian striker Ranti Martins in the 26th. Brazilian Roberto Silva fired the visitors ahead in the 62nd minute only to see Mamoudou Camara equalise in 69th minute.
Just as the two sides looked set to split points, Lawrence deflected a Jose Estefane’s shot into his own goal in the 80th minute. The result leaves Bahrain’s Al Muharraq on top of Group A with four points after they drew with Al Ansar. They had earlier beaten Sur 3-2 in their first match.
Dempo and Sur are tied on three points though the Goan side are second placed thanks to their better goal difference.
Sur got the lead when Ivory Coast striker Traore latched on to a long ball to beat goalkeeper Abhijit Mondal from inside the box. Down by a goal, the visitors applied pressure on the hosts and created a couple of chances only to see Martins and his strike partner Chidi Edeh fail to finish the moves.
Chidi shot over the crossbar from close range after some good work by him and Martins. Repeated Dempo onslaught, however, paid off when a Martins header found the back of the net off a Nicolau Borges free-kick.
After the breather, Dempo were still attacking and hardworking Brazilian midfielder Roberto Mendes Silva scored following a neat interplay with Martins. Martins could have increased his side’s lead but his shot was cleared off the line by defender Ali Al Farsi.
Sur came back into the match when Mamoudou Camara fired a low shot to beat Mondal, and ten minutes from the long whistle, they got the winning goal, thanks to Lawrence’s error.