Gautam Gambhir made 97 and Captain Mahendra Singh Dhoni smashed an unbeaten 91 off 79 balls as
for the first time since 1983 with a six-wicket victory over Sri Lanka on Saturday.
Sri Lanka, who won the toss and elected to bat in the day-night final, rode on Mahela Jayawardene's 103 not out off 88 balls to pile up 274-6 in their 50 overs.
India, cheered by a sell-out crowd of 33,000 at the Wankhede stadium, surpassed the challenging target with 10 balls to spare as Dhoni pounded Nuwan Kulasekara for the winning six.
India had slumped to 31-2 by the 6th over when sling-arm fast bowler Lasith Malinga dismissed Virender Sehwag (0) second ball and had star batsman Sachin Tendulkar (18) caught behind in his 4th over.
Gambhir, who was dropped on 30 and escaped a run-out chance on 49, turned the match around by adding 83 for the third wicket with Virat Kohli and 109 for the fourth with Dhoni.
Yuvraj Singh, who was named the man of the tournament, partnered his skipper till the end with 21 not out after Gambhir was bowled by Thisara Perera in the 42nd over when 52 more were still needed.
Dhoni's men emulated Kapil Dev's compatriots who won the 1983 World Cup by beating the West Indies in the final at Lord's in London.
The victory, watched by Indian President Pratibha Patil and Sri Lanka's head of state Mahinda Rajapakse, was the first occassion a team had won the tournament on home soil.
It was only the third time in 10 World Cup finals that a side batting second had chased down the victory target.
The finale gave Tendulkar, the world's most successful Test and one-day batsman, his first World Cup title in six appearances since 1992.
The defeat ended Sri Lankan star bowler Muttiah Muralitharan's dream of being part of a second World Cup-winning team, having won the title under Arjuna Ranatunga in 1996 in Lahore.
Muralitharan, who turns 39 next month, went wicketless in eight overs to end his career with a record 800 Test and 534 one-day wickets.
Confusion reigned at the toss, which had to be performed twice after match referee Jeff Crowe did not hear Sri Lanka captain Kumar Sangakkara's call when Dhoni threw up the coin.
Jayawardene shored up Sri Lanka's innings before tailenders Nuwan Kulasekara (32 off 30 balls) and Thisara Perera (22 off nine) helped their team smash 63 runs in the last five overs of power-play.
India's left-arm seamer Zaheer Khan dried up the flow of runs at the start and his two wickets made him the tournament's leading bowler alongside Pakistan captain Shahid Afridi with 21 wickets each.
Zaheer opened with three successive maidens and then struck with the first ball of his fourth over when Sehwag dived to his right in the slips to remove Upul Tharanga for 2.
Fast bowler Shanthakumaran Sreesanth lifted the pressure by conceding 15 runs in his fifth over that included a no-ball and a warning for running in the danger area in his follow-through.
Sreesanth, who was preferred ahead of spinner Ravichandran Ashwin after Ashish Nehra was ruled out with a fractured finger, was thrashed for 52 runs in his eight overs.
Tillakaratne Dilshan, going into the final as the tournament's leading scorer with 467 runs, made 33 when he was bowled by off-spinner Harbhajan Singh to make Sri Lanka 60-2 in the 17th over.
Jayawardene put on 62 for the third wicket with Sangakkara (48) and 57 for the fourth with Thilan Samaraweera (21).
V Sehwag
AJ Strauss
TM Dilshan
AB de Villiers
LRPL Taylor
RN ten Doeschate
KJ O'Brien