The two-time champion, Chennai comfortably managed to overhaul Mumbai's 173 with eight balls to spare at the Brabourne Stadium to set up a meeting with Kings XI Punjab at the Wankhede Stadium on Friday.
Raina, the only player to score 400 runs in all the IPL seasons, scored a quick-fire 33-ball 54 which was laced with four fours and two sixes. He was ably supported by David Hussey, who also remained unconquered on 40 off 29 balls.
Chennai began their run chase by scoring at a brisk pace. Openers Dwayne Smith and Faf du Plessis laid a strong foundation by scoring 60 runs off just 38 balls.
But Mumbai wrested the momentum when veteran off-spinner Harbhajan Singh dismissed the two in the seventh over. Smith struck four fours for his 20-ball 24, including three consecutive ones off Jasprit Bumrah before being caught on long on by fellow West Indian Kieron Pollard.
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They were further reduced when they lost New Zealand skipper Brendon McCullum at a score of 87, three overs later. McCullum struck two sixes in his 11-ball 14 before being stumped off left-arm spinner Pragyan Ojha.
One-down batsman Raina and Hussey did the repairing job and the duo carted the bowler all over the park to comfortably guide their team to victory.
Harbhajan Singh was the pick of the bowlers, grabbing two wickets for 27 runs.