Goossens scored the decisive goal in the 88th minute as he headed home after Dudu Omagbemi's shot hit the crossbar and rebounded at the Shiv Chhatrapati Sports Complex Stadium.
NorthEast United, who had come here after impressive shows against Mumbai FC and Delhi Dynamos in their away matches, had more ball possessions but they had very few scoring chances.
With the win, Pune FC jumped to the fourth spot with seven points from five matches while NorthEast remained on third position with eight points from six matches.
NorthEast United goalkeeper T P Rehenesh, who saved at least three brilliant saves against Delhi Dynamos, was also up to his task today, including a brilliant save of a Davide Colomba shot on the line.
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Greek World Cupper Konstantinos Katsouranis was impressive at the centre of the park for Pune while winger Israel Gurung made some threatening moves.
Both teams endured a nervy start but Pune settled down sooner. The visitors later picked up the tempo and threatened on the counter.
Pune's perseverance finally paid off at the death when Dudu smashed his shot against the crossbar which rebounded for Dutchman Goossens to head into an empty net.
The home side then managed to hold on through the five minutes of injury time for their second win of the tournament.
Italian Davide Colomba was sent off by the referee for trying to delay a NorthEast throw in in the dying minutes of the match.