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De Villiers faced 40 balls and hit five boundaries and one six.
Pace bowlers Munaf Patel and Dimitri Mascarenhas and legspinner Shane Warne each took two wickets apiece for Rajasthan.
De Villiers -the only batsman to have struck a century in the tournament so far - came in with Delhi reeling on 4-48.
But he immediately took the attack to the seamers and boosted Delhi's score to 5-105, hitting strongly on the off side. The 25-year-old South African right-hander was dismissed by Warne in the 16th over attempting to sweep past short leg.
Delhi lost their first wicket in just the second over when opener Gautam Gambhir on 8 nicked a Mascarenhas slower delivery to Warne in the slips.
Three balls later Mascarenhas struck again, deceiving Virender Sehwag with a slower ball as he attempted to hit over the top and he was caught at mid-on by Kamran Khan for 16.
Warne claimed his first wicket in the eighth over when he took a return catch from Dinesh Karthik for 4. Delhi then slumped to 3-38 when Tillakaratne Dilshan became Patels first wicket, caught by Swapnil Asnodkar for 7.
Batting at number six, Daniel Vettori scored 29 from 28 balls to further bolster the score. He was dismissed by Patel in the 19th over, missing a full length delivery to be clean-bowled.
