Santner and Mitchell are also members of the New Zealand squad which will meet the West Indies in three Twenty20 internationals starting Friday.
CSK, already out of the reckoning for the first time ever, will aim to end their dismal campaign on a positive note.
Super Kings posted 175 for five on Sunday night and Dhoni led the team's recovery from 27 for three with an unbeaten 75 off 46 balls. The hosts restricted Royals to 167 for eight to win the game by eight runs.
New Zealand inflicted a rare 5-0 one-day international series whitewash over Pakistan on Friday with a 15-run win at Wellington's Basin Reserve
After a strong start, when they reached 231 for two, they lost their last eight wickets for 88 runs as they chased a monumental 386 to make New Zealand bat again.