Finch got good support from Karthik (40 off 28) as the duo shared a 92-run stand for the fourth wicket after Lions were reduced to 56 for three in the seventh over.
Opener Ishan Kishan chipped in with a 25-ball 34 before leggie Amit Mishra had him caught at short fine leg off a googly.
Finch was the stand out the batsman for the Lions who were put in to bat by Daredevils in the first of the two matches to played at the Green Park stadium.
He went on to hit two more sixes with last one bringing up his second half century of the season. Finch also hammered four boundaries in his entertaining knock.
Karthik was scoring freely at the other end, allowing Finch to play at the other end.
The wicket-keeper batsman missed out on his third half century this season after being caught at long-on off Carlos Brathwaite.
Finch was dismissed in the penultimate over of the innings, missing a fuller one from Mohammed Shami to be bowled.
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