The 27-year-old opener hammered an unbeaten 133 in a stunning display of aggressive batting as the West Indies made a mockery of South Africa's challenging total of 258-8 to win the semi-final with six overs to spare.
Defending champions West Indies will clash with Australia in the final at Mumbai on Sunday.
Gayle reduced the day-night match to a no-contest with his breath-taking strokes on both sides of the wicket, hammering three sixes and 17 fours in a 135-ball knock for his 15th century in 150 one-day internationals.
"Once I get a start I always try to capitalise on it. I like challenges and this was a good one. This was definitely one of my better knocks," said Gayle, named man of the match.
Gayle received valuable support from Shivnarine Chanderpaul, who cracked a solid 57 before retiring hurt with cramps. They added 154 to ensure the West Indies keep their reputation intact of beating South Africa in big events.
The West Indies defeated South Africa in the 2003 World Cup and then in the Champions Trophy in England the following year. The defeats contributed to South Africa's failure to reach the semi-finals on both the occasions.
A top batsman
"He [Gayle] is an excellent batsman and a great influence on the guys. He takes everything seriously," said West Indies skipper Brian Lara.
"The plan was not to lose early wickets since South Africans had gained the upper hand by taking early wickets in their previous games."
South Africa earlier rode of Herschelle Gibbs's impressive 77 to post their highest total in the tournament, but were later reduced to a state of helplessness by Gayle's pyrotechnics.
Fast bowlers had played crucial roles in South Africa's victories in the last two group matches against Sri Lanka and Pakistan, but looked clueless against left-handed openers Gayle and Chanderpaul.