Chennai will now have to win both their remaining matches to have any chance of making it to the semifinals.
Bodi and Neil McKenzie (32) shared a 93-run stand for the third wicket from 9.5 overs to turn the tide in favour of the Lions.
The Lions needed 51 from the last five overs and 20 from the last two overs and they did it in style by reaching 159 for four with three balls to spare.
For Chennai, Ravichandran Ashwin and Albie Morkel took a wicket each, besides the two wickets by Bollinger for 18 runs.
Image: Highveld Lions Gulam Bodi reacts as he makes fifty runs against the Chennai Super Kings, during a Champions League Twenty20 match, in Cape Town, South Africa, Tuesday, Oct 16, 2012.