Chennai were beaten in a Super Over by Australia's Victoria Bushrangers at St George's Park on Saturday after both teams scored 162 in 20 overs.
Dhoni entrusted the shoot-out over to off-spinner Ravichandra Ashwin, who conceded 23 runs, 22 of them scored by Victoria captain David Hussey.
Chennai could only manage 13 off Victoria medium-pacer Clint McKay.
It set up a situation where three teams could finish with three wins each in Group A - Chennai, Victoria and South African champions the Eastern Cape Warriors.
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Victoria play Wayamba Elevens in Centurion on Monday and will be favourites to beat the Sri Lankans, who have lost both their games so far.
Chennai meet the unbeaten Warriors in Port Elizabeth in the last round robin match of the tournament on Wednesday in what shapes up as a crucial encounter.
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The Warriors completed their third successive win in the early match of Saturday's double-header when they defeated New Zealand's Central Stags by six wickets.
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