Smith hammered six sixes in his whirlwind knock and shared an 85-run stand with Dinesh Karthik (26 off 30) after Lions lost their top three batsmen for nine runs. All-rounder Shane Watson was the stand out bowler for the hosts, ending with four wickets for 29 runs in his four overs.
RCB, confident of chasing any total at home, were on top of the opposition after putting them in at the Chinnaswamy Stadium.
McCullum stepped out on the first ball Abdulla bowled and ended up being holed out at deep extra cover with the safe hands of AB De Villiers doing the needful. Finch departed three balls later as he tried a flick off one that turned away, only to be caught at first slip by Chris Gayle.
The Lions were in deeper trouble in the fourth over when Watson removed their captain Suresh Raina, who has been the leading run getter for his side in the competition. Raina fell to a short ball again as he pulled Watson straight to the man at short fine-leg.
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Karthik, at the other end, played the supporting well until he shuffled across the stumps to lap it towards fine leg, only to play on to his stumps. His shot selection was questionable with a man at deep fine leg in place.
Smith was the lone hope left for Lions but he too departed while attempting another big one off leggie Yuzvendra Chahal. Besides a barrage of sixes, he ended up hitting five boundaries.
Eklavya Dwivedi did his bit towards the end by smashing 19 off nine balls.