Muhammed Nemil was the lone goal scorer at a rainy, blustery Kishore Bharati Krirangan here.
With the win, Goa join Mohammedan Sporting and Bengaluru FC with three points in Group A, even though the latter have a game in hand.
Jamshedpur FC is the other team in the group. The top two teams from each Group qualify for the quarter-finals.
The Gaurs got their goal early through Nemil, who struck his second in two games in the tournament.
The move came from the right when Mevan Dias broke through and delivered a minus inside the box finding his classy centre-forward in space. Nemil turned, transferred the ball to his favoured left-foot and found the bottom corner with precision.
He could have made it three for the tournament 15 minutes later, but this time his curler from just outside the box, missed narrowly.
In the second-half, the Airmen did try and apply some pressure but the organised and well-schooled Gaurs defence held firm.
The Air Force upped the ante in search for an equaliser and in the final 10 minutes got several chances to draw level. Mohd. Aqib first hit the cross-bar and then substitute Prabhjot Singh unleashed a wonderful free-kick, drawing a fantastic save from Goa keeper Hrithik Tiwari.
The Air Force got as many as three corners as well in the last few minutes but couldn't cash in.
Sudeva FC and Kerala Blasters play out a draw
Sudeva FC and Kerala Blasters were forced to split points after Md. Ajsal's 42nd minute strike was cancelled out by Mangku Kuki, who scored just three minutes later.
Sudeva coach Chencho Dorji made his attacking intentions clear from get go, opting for a four-man midfield and a three-man forward line while the Blasters' gaffer had no such illusions going in with a regulation 4-4-2.
Sudeva dominated possession in the first half and had the larger share of attacks but could not press home the advantage.
It was then that the Blasters struck against the run of play with barely three minutes to go for the first half to end.
Ajsal received the ball in front of the box and drove in, shooting from near the penalty spot area to beat keeper Kabir Kohli and put Sudeva ahead.
The response was immediate. Kuki received the ball on the right from a quickly taken throw-in in the attacking third to gracefully curl it into the top corner to draw parity.
Sudeva continued to dominate possession in the second-half and created more chances but there was a period when both teams sat back and wanted to control possession which might have affected the end result.
The Delhi NCR side threw everyone forward in the final minutes of the game but beyond some set-pieces, nothing fruitful materialized and the stalemate remained for the first draw of the tournament after six games.