The all-important goal was scored by Abranches in the 90th minute off a pass from substitute Romeo Fernandes.
Both the teams played cautiously in the barren first half which saw the play confined to midfield.
Dempo, who lost their top position to East Bengal after they lost to ONGC, failed to dominate the midfield in the absence of midfielders Climax Lawerence and Rohan Rickett.
Air India came near to breaking the deadlock in the dying minutes of the first half, but a Micky Fernandes shot from a free kick hit the bar.
The second half was more lively and Dempo twice had clear chance to take the lead after resumption.
But a Ryuji Suueoka tap from close off Clifford Miranda cross was kept out by rival keeper Sukhwinder Singh.
Abranches followed the ball on the left, but his shot came off the far post before the ball rolled back into the arms of the Air India keeper on the near post.
Air India's Junior had an opportunity to score but he headed straight into the hands of rival keeper Tyson Caidao.
Both the teams introduced fresh pairs of legs to break the deadlock and Dempo finally scored in the 90th minute through Joaquim Abranches after Peter Carvalho failed to direct his header on target off substitute Romeo Fernandes cross.
Ryuji Suoeka laid a pass to substitute Romeo Fernades who in turn passed to Abranches who shot home from inside the box to give Dempo full points and take them to second place with 13 points from seven matches, one point below East Bengal who are at the top with 17 points. Air-India remained at the bottom with three points from six matches.
