CSK dished out a disciplined bowling and fielding effort to first restrict DC to 147 for nine and then chased down the target with ease, reaching 151 or four in 19 overs.
Delhi Capital now face Chennai Super Kings in the second Qualifier in their bid to make it to the maiden IPL final against Mumbai Indians.
Rajasthan are officially out of the tournament, finishing with just 11 points from 14 games.
After making just 27 runs in Powerplay overs, the hosts eventually put on board a fighting 179 for four and dismissed Capitals for just 99 in 16.2 over to snatch the top spot from the visitors.
It was Delhi's eighth win in 12 games, giving them the 16 points needed to seal a top-four berth. Chennai Super Kings were the first team to quality for the play-offs.
With this win, Delhi Capitals now lead the points table with 14 points while Rajasthan Royals lie at the seventh spot.
Hardik and Krunal Pandya came up with an all-round show while Rahul Chahar returned with figures of 3/19 as Mumbai beat Delhi by 40 runs at the Kotla
Shikhar Dhawan found form with a 63-ball 97 and powered Delhi Capitals to a seven-wicket win over Kolkata Knight Riders in the IPL here Friday, leaving two legends at the visiting dugout beaming.
Royal Challengers Bangalore made 149 for eight but could not defend the total with Delhi Capitals winning by four wickets.
The win took Sunrisers' overall head-to-head record against Delhi at the Feroz Shah Kotla stadium to 4-1.
Kings XI Punjab's costliest buy Sam Curran proved his worth with an incredible spell at the back end as the home team pulled off a miraculous 14-run victory against Delhi Capitals.
Prithvi Shaw slammed 99 while Kagiso Rabada defended 10 runs in the Super Over as Delhi Capitals beat Kolkata Knight Riders by 3 runs.
Chennai Super Kings used the conditions at the Ferozeshah Kotla beautifully as they beat Delhi Capitals by six wickets on Tuesday.
Pant's unbeaten 27-ball 78 was too much to handle for Mumbai as they failed to get going in their humongous chase of 214.
Four children and a woman were killed and at least seven injured after a four-storey building collapsed in northwest Delhi's Ashok Vihar Wednesday, police said.
A dust storm, with winds gusting up to 96 kmph, barrelled through the national capital this evening, causing flight diversions, disrupting Delhi Metro services and uprooting trees.
Set a target of 175, Mumbai Indians crumbled against quality leg-spin bowling by Sandeep (3/36), Amit Mishra (3/19) and medium pace of Patel (3/28).
In a dead rubber, Delhi Daredevils prevailed victorious over second-placed Chennai Super Kings as the bowlers did a brilliant job to restrict the batsmen, defeating them by 34 runs at Kotla.
Virat Kohli and AB de Villiers struck brilliant half-centuries to lead Royal Challengers Bangalore to an easy five-wicket victory.
Sunrisers Hyderabad outclassed Delhi Daredevils by nine wickets to consolidate their position on the top of the IPL 2018 Points Table at the Feroz Shah Kotla.
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