Mumbai Indians recovered from a poor start to post a competitive 183 for seven but Smith (62 runs off 30 balls) and Mcullum (46 off 20) ensured Chennai Super Kings chased down the target with 20 balls to spare.
The lone bowler who stood out in the high-scoring game was Super King Ashish Nehra, who took three wickets for 23 runs in his four overs.
It was Super Kings' third victory in as many games while Mumbai Indians suffered their fourth loss in a row.
The game was only going Super Kings' way with way Mcullum and Smith toyed with Mumbai Indians bowling attack. McCullum hammered four sixes and eight boundaries while McCullum was not far behind with six fours and two sixes.
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Earlier, blistering half centuries from captain Rohit Sharma and Kieron Pollard enabled Mumbai Indians recover from a poor start.
While Sharma batted in his usual forthright manner to hit five fours and a six, Pollard collared the Super Kings attack to strike five sixes and four fours.
The initial recovery work was laid by a quick 24 off 21 balls by Harbhajan Singh, who was surprisingly promoted ahead of the big West Indian.
The bit-hitting of Pollard, in particular, not only regaled the big crowd but also helped Mumbai add 121 runs in the second half of the innings after they were 62 for 4 after ten overs.
Super Kings' bowling looked clueless on how to stop Pollard and but for a top-drawer bowling stint by Ashish Nehra, who grabbed three for 23, while Jadeja went for 49 runs, including 26 in his fourth over, Ashwin conceded 13 in his only over. The other World Cup regular, Mohit Sharma, gave away 43 runs for one wicket.