Every Test match win by runs does not mean that the team wins by a huge margin. There may be some instances where a team win by a small margin. The smallest margin of win was by 1 run by Windies against Australia in 1993 at Adelaide.
Recently, India defeated Australia by 31 runs at Adelaide on 10 December 2018. Cheteshwar Pujara was the Player of the Match.
Let us have a look at the top 5 closest wins for India in Tests (by runs).
#5 49 runs against Windies, Kingston, 2006
India scored 200 in the first innings of the match against Windies on 30 June 2006 at Kingston. Rahul Dravid was the highest scorer in the match. He scored 81 in this match. Jerome Taylor picked a fifer by dismissing Wasim Jaffer, Yuvraj Singh, Mohammad Kaif, Sreesanth and Munaf Patel.
However, Windies suffered a worse collapse in the batting as they scored 103 all out. Harbhajan Singh picked a 5-wicket haul by dismissing Daren Ganga, Dwayne Bravo, Ramnaresh Sarwan, Denesh Ramdin and Pedro Collins.
India's second innings was bundled out for a total of 171 with Dravid being the highest scorer. He scored 68. Corey Collymore was the star performer with the ball. He dismissed VVS Laxman, Yuvraj Singh, Anil Kumble, Rahul Dravid and Harbhajan Singh.
In reply, Windies made a strong comeback. Sarwan and Ramdin scored 51 and 62* respectively. But it was not enough as they were dismissed for 219 and lost by 49 runs. Kumble picked a 6-wicket haul by dismissing Chanderpaul, Bravo, Samuels, Taylor, Collins and Collymore.
Rahul was the Player of the match for his fifties in both the innings and India won the 4 match series by 1-0.
#4 37 runs against Windies, Port of Spain, 2002
India scored 339 in the first innings of the match against Windies on 19 April 2002 at Port of Spain. Tendulkar scored another century and was dismissed by Cameron Cuffy leg before wicket. Laxman scored an unbeaten 69. Marlon Black and Adam Sanford picked up 3 wickets each.
Windies scored 245 all out. Brian Lara and Carl Hooper scored half-centuries. Javagal Srinath was the star performer with the ball by dismissing Gayle, Chanderpaul and Murray.
India were bundled out for 218 in their second innings. Tendulkar remained unbeaten with 75. Laxman scored 74 and was bowled by Mervyn Dillon. Dillon was the star performer with the ball by dismissing Das, Laxman, Srinath and Nehra.
Windies made a strong comeback. Gayle and Chanderpaul scored half-centuries. But they were 37 runs short of the target. Javagal Srinath and Ashish Nehra picked up 3 wickets each.
Laxman was the Player of the match for his fifties in both the innings and India led the 5 match series by 1-0.