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Auckland: Raina's 104-ball 110 and Dhoni's 76-ball 86 in helped India chased down 288 with 8 balls spare, and still unbeaten in World Cup.
The win had no influence on the group standings as India were assured of top place in Pool B regardless of the result while Zimbabwe had already been eliminated.
Zimbabwe captain Brendan Taylor was the day's individual hero, celebrating his last international before taking up an English county contract by scoring 138 in his team's 287 all out from 48.5 overs.
Taylor reached his eighth one-day international hundred, a Zimbabwe record, with a ramp shot off Mohammed Shami which steered the ball over third man for a six. He was also the first Zimbabwe batsman to score consecutive centuries in a World Cup.
The Zimbabwe skipper then struck three fours and two sixes off an over from left-arm spinner Ravindra Jadeja to become the second-highest run scorer in the tournament before he was caught off Mohit Sharma.
Taylor added 93 for the fourth wicket with Sean Williams (50) who hoisted three sixes to leg off Ravichandran Ashwin before the off-spinner took his revenge by holding a sharp caught-and-bowled chance.
Opening bowler Tinashe Panyangara rocked the Indians by capturing the wickets of openers Rohit Sharma (16) and Shikhar Dhawan (4) in the same over.
Ajinkya Rahane (19) played some handsome drives before he was run out trying to regain his crease after a misunderstanding with his partner Virat Kholi.
India were in trouble when Kholi was bowled around his legs for 38 trying to sweep off-spinner Sikandar Raza before Raina found his timing to hit Williams's left-arm spin into the crowd from successive deliveries.
The burly left-hander received a let-off on 47 when Hamilton Masakadza dropped a simple chance off Raza at short fine-leg from a top-edged sweep.
Raina hit a huge six into over wide long-on while Dhoni hit hard and ran harder as the pair brought up their ninth century partnership in one-day internationals.
The Zimbabwe fielding began to falter and the bowling became more erratic and Raina completed his first World Cup century and his fifth in one-day internationals from 94 balls. Dhoni secured the victory with eight balls to spare by hooking a six.
Earlier, India have won the toss and opted to field.
Both teams unchanged.
Teams:
Zimbabwe: Chamu Chibhabha, Sikandar Raza, Hamilton Masakadza, Brendan Taylor (Capt. & wk), Sean Williams, Craig Ervine, Solomon Mire, Regis Chakabva, Tinashe Panyangara, Tawanda Mupariwa, Tendai Chatara
India: Shikhar Dhawan, Rohit Sharma, Virat Kohli, Ajinkya Rahane, Suresh Raina, MS Dhoni (Capt. & wk), Ravindra Jadeja, Ravichandran Ashwin, Mohit Sharma, Mohammed Shami, Umesh Yadav
