Veteran Jhulan Goswami starred with the ball with three wickets, helping India dismiss South Africa for a paltry 156 in 40.2 overs.
Raut (70 off 92 ) and Raj (62 off 79) then delivered with the bat, taking their team to a comfortable win in 33 overs after a rather jittery start to the chase.
The win got sweeter considering India had lost to South Africa in the league stage once en route the final.
Captain Raj not only guided the team to a resounding win but also became the first Indian captain to lead the side in 100 ODIs.
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The tournament also turned out to be good preparation for India ahead of the World Cup, which begins in the UK next month.
Both Raut and Raj displayed top form throughout the tournament. Raut had scored an unbeaten 109 against Ireland while Raj came to the final after scoring two half-centuries.
Chasing a modest target, India lost opener Deepti Sharma and Mona Meshram cheaply before Raut and Raj completed the job in a clinical fashion.
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