De Kock topscored with 44 runs and de Villiers added 40 as the visitors looked for a 2-0 sweep in the two-match series after winning the Sunday's opening game by 52 runs.
Left-arm spinner Arafat Sunny forced de Kock into chipping a catch to Sabbir Rahman at midwicket to earn Bangladesh's first breakthrough in the 11th over.
Left-handed de Kock faced 31 balls and hit four fours and two sixes in his innings.
JP Duminy got a leading edge off the second ball of the over to hoist a catch which Shakib Al Hasan gleefully accepted at short midwicket to remove him for six.
AB de Villiers gloved the next ball to wicketkeeper Mushfiqur Rahim to end his 34-ball innings which included six sixes.
David Miller survived a strong caught behind appeal in the same over to put on 34 runs for the fourth wicket with skipper Faf du Plessis (16).
Nasir finished with 2-26 for Bangladesh.
South Africa handed leg-spinner Eddie Leie a Twenty20 international debut for Kagiso Rabada.
Bangladesh also made one change as batsman Rony Talukdar replaced off-spinner Sohag Gazi to make his debut.
