With the match heading to a tame draw, Salgaocar's Gilbert Oliveira and Darryl Duffy struck a goal each in the extra time to help themselves save the relegation.
Salgaocar who finished with 24 points from 20 matches finished seventh, while Dempo remained on 19 points and got relegated. There is no relegation for New entrant Bharat FC who finished last.
Derrick Pereira named an unchanged line-up from the one that downed Bharat FC 5-1 last weekend. Meanwhile, Trevor Morgan made two changes with Peter Carvalho and Tolgay Ozbey coming in for Lenny Rodrigues and Joy Ferrao.
They had the first chance in the third minute when Rowilson Rodrigues' rasping long ranger was just about averted by Karanjit Singh.
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The next opportunity was created by the home side as Darryl Duffy split the opposition defense to put Umesh Harijan through. However, the youngster's shot from close range was saved.
Ozbey then tested Karanjit in goal from close range with a powerful shot but the Salgaocar custodian once again came to his team's rescue.
Francis Kasonde made a goal-line clearance after Karanjit Singh failed to deal with a long ball. Alwyn George was at hand and struck the ball goalwards but Kasonde acrobatically cleared just in time in the 37th minute.
Four minutes later, Ozbey was allowed a lot of space to maneuver and the Australian dribbled past a heave of defenders to shoot but the ball struck the goal post to go out for a goal-kick.
The very next minute, Duffy doubled the lead for the home side. He lofted the ball over the Dempo custodian after getting into an one-o-one position, thanks to a daft mistake by Rowilson Rodrigues.