Pandey remained unbeaten on 83 off 49 balls with the help of seven fours and three sixes but could not lead his team to an imposing total as Sunrisers managed only 51 runs in the last six overs after Warner's dismissal.
Warner cracked his seventh fifty this season, accompanying Pandey for a 115-run stand for the second wicket which formed the bedrock of Sunrisers' innings after CSK skipper M.S. Dhoni put them into bat.
For CSK, Harbhajan Singh was the pick of the bowlers with figures of 2/39 in four overs.
The visitors lost Jonny Bairstow (0)—playing his last IPL game—early, as the England stumper-batsman was out caught behind trying to cut Harbhajan.
From there on, Warner and Pandey paced their innings perfectly as Sunrisers raced to 91/1 at the halfway stage.
Harbhajan removed Warner in the 14th over with a slower one which the veteran Australian failed to read and came down the track only for Dhoni to effect a brilliant stumping.
Vijay Shankar (26; 20b, 4x2, 6x1) then joined hands with Pandey for a 47-run partnership before holing out to Ravindra Jadeja at deep midwicket off Deepak Chahar.
Shankar never really got going and after he was removed, Yusuf Pathan (5 not out) also could not up to the ante.