Opting to bat after the coin landed in skipper Mahela Jayawardene's favour, Delhi lost wickets at regular intervals to leave the hosts with a real chance of consolidating their position in the points table.
The total is the lowest in this edition of the Twenty20 league.
This is also the second time in a this edition that Daredevils have been dismissed for less than 100 -- the first one coming against Chennai Super Kings at the Feroz Shah Kotla last month.
The first casualty was the skipper himself, trapped in front of the wicket by Ishant Sharma after what appeared to be a watchful start to the visitors' innings in yet another must-win game.
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Next to go was Virender Sehwag, whose off-stump was disturbed by Darren Sammy, who celebrated the big wicket by performing his by-now-familiar act -- sucking on a pacifier hanging around his neck.
With the two big guns gone, the onus was on David Warner to lead the resurrection act, but the Australian was stumped off Amit Mishra's bowling.
The rest of the batting could not stand up to to Steyn and Co as they were bowled out in 19.1 overs.
That Mahela Jayawardene's six over square-leg was the only maximum of the evening, was another poor advertisement from the the league's point of view.
Delhi have so far won three matches while losing seven.