Having won the toss, Chennai chose to put their opponents into bat first, and were set a target of 155 for victory.
Ashish Nehra was the pick of the Super Kings' bowlers, finishing with three wickets for 33 runs from his four overs.
Chennai got off to a quick start in their reply, with Dwayne Smith and Faf du Plessis putting on a 57-run partnership for the opening wicket, with the latter going on to complete a half-century.
MS Dhoni almost reached the 50-run mark as well, but the Super Kings reached their target with over two overs to spare before he could claim a half-century.
Chennai sit second in the points table, having already qualified for the playoffs.