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With England needing 43 from the last 18 balls to beat New Zealand on Friday, Will Jacks and Rehan Ahmed put on an unbeaten partnership of 44 from 16 balls to secure the win.
In the previous two games, England made a below-par 146-9 against Sri Lanka only to dismiss their co-hosts for 95 to secure victory, and were 58-4 against Pakistan before Brook himself hit a stunning century.
Those three victories followed a group stage where England struggled to beat Nepal, Scotland and Italy and were beaten by West Indies.
Their success also follows the dismal Ashes tour of Australia in Test cricket.
"I don't believe we need a perfect game to win the competition," said Brook, who is leading England for the first time at a World Cup.
"We've won those tight games which in World Cups prove to be very important and we've got a lot of confidence going into the deeper parts of the game.
"We've got a lot of competitive lads. Everybody wants to win, which is a given really, but even off the field when we're playing golf, playing cards, whatever, everybody is always really competitive and they always have that slight edge and they take it out into the cricket as well."
Brook said he expects Thursday's atmosphere to be "awesome", with the match to be played at the iconic Wankhede Stadium in front of 33,000 spectators.
England resisted naming an XI before the toss, but seam-bowling all-rounder Jamie Overton appears likely to replace leg-spinner Ahmed.
India were the overwhelming pre-tournament favourites but have also stuttered at times in the competition.
They were given a scare by the United States in the group stage and were well beaten by South Africa in the Super 8s.
"I said the other day there's a lot of pressure on both sides, potentially more on them going into here with the crowd and the disappointment they had against South Africa as well," Brook said.
"But we're just going to go out there, stick to what we know and assess conditions as quickly as possible and give it real good fight."
