Smith (51 not out from 37 balls) held the innings together as openers Ajinkya Rahane 46 (41b; 4x4, 1x6) and Rahul Tripathi 38 (23b; 7x4) played important knocks. Smith's half century was laced with four boundaries and a six.
Chinaman bowler Kuldeep Yadav (2/31) was the pick of the bowlers for KKR.
Pune openers recovered from a tentative start against KKR new ball bowlers with Tripathi playing the aggressor's role after being dropped on 35 by Yusuf Pathan off Colin de Grandhomme's delivery.
The in-form 26-year-old right-hander took a liking to pacer Umesh Yadav, hitting three fours, two in one over, to race to 38 off just 22 balls before leg-spinner Piyush Chawla outfoxed him with a googly that the batsman chopped onto his stumps trying to cut.
At the other end, Rahane looked steady for his knock but fell short when Sunil Narine went wide outside off stump to force him to come down the ground and get stumped by wicketkeeper Robin Uthappa.
Rahane was part of two vital partnerships, with Tripathi for a 65-run stand for the first wicket and with Skipper Smith for a 47-run second-wicket stand.
Mahendra Singh Dhoni played a quickfire 23 (11b 1x4 2x6) before Kuldeep got the back of the former India captain with a googly as Uthappa stumped him.
Dan Christian 16 (6b 0x4 2x6) hit big too before getting out off the last delivery as KKR leaked 30 runs in the last two overs. Christian tonked two sixes to take his side to a par score on this wicket.
Brief scores: Rising Pune Supergiant 182/5 (Steve Smith 51 not out, Ajinkya Rahane 46; Kuldeep Yadav 2/31) vs Kolkata Knight Riders.