Samson, only brought into the XI due to Rinku Singh's absence after the death of his father, struck an unbeaten 97 to help India chase down a target of 196 to win by five wickets.
The victory meant India leapfrogged the Windies into second position in their Super 8s group and into a semifinal place where they will meet England in Mumbai on Thursday.
Speaking to reporters after the game, Gambhir said: "He's a world class player, we all know how good a player Sanju is.
"It was all about backing him. When the team needed him the most - obviously today was the day - he showed his full potential.
"I actually felt that he never accelerated the innings. It was just very normal cricketing shots and I never saw him muscling the ball as well. That is the kind of talent he has.
"Obviously he had a tough series against New Zealand, so sometimes it's important to give him a break as well, because you want to get the guy off that pressure situation as well.
"And we always knew that whenever we needed him in the World Cup game, he'll come and deliver it for us."
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Sanju Samson produced a sensational unbeaten 97 to guide India national cricket team into the T20 World Cup semi-finals with a dramatic five-wicket victory over the West Indies cricket team in a high-scoring encounter at Eden Gardens on Sunday.
The Proteas will move into the semi-finals of the ICC Men's T20 World Cup with their unbeaten record intact after a hard-fought five-wicket win over Zimbabwe on Sunday.
