A timely 59-run run stand between Suresh Raina (53 not out of 36 balls) and Aaron Finch (26) secured the game for Lions after Smith put a stellar show with the ball, ending with career best T20 figures of four for eight.
Lions eventually raced home in 13.3 overs after restricting to KKR to 124/8 at the Green Park Stadium, which hosted its first ever IPL game.
The modest chase was going to be a tricky one under the conditions.
The Lions lost their star bowler on the day, Smith, after he got an inside edge to the keeper while attempting a pull on the first ball of the innings. Pacer Ankit Rajpoot provided the important breakthrough.
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The other dangerous opener Brendon McCullum too did not hang around for long after hitting a six. Morne Morkel went through the gate of Dinesh Karthik to have Lions in a spot of bother at 38 for three in the fourth over.
With run rate pressure not there, the two batted sensibly to take the team at the doorstep of victory. Finch was unlucky to be run out after he collided with Raina as the pair attempted a third run.
(REOPENS DEL 120)
Earlier, Smith turned out to be almost unplayable for KKR batsmen after Raina put the opposition on a greenish track.
The Lions made good use of the conditions with the ball moving around.
Smith then dealt a triple blow to leave KKR at 55 for four in 10 overs. The gentle medium pacer the odd ball seam and jump off the pitch as he had Manish Pandey caught at first slip before Uthappa played a loose shot to be caught behind.
Smith dominated the opposition batsmen and ended up bowling 18 dot balls in his four over spell.
The in-form Yusuf Pathan (36) and Suryakumar Yadav (17) were able to stitch a handy 41-run partnership but their team needed more from them in the circumstances.
KKR could have got a few more if Pathan did not get out on the second ball of the 18th over. The big hitter ended with three fours and a six in his run a ball effort.