Chasing a modest 142 to win, Delhi achieved their target with 17 balls to spare and the loss of just four wickets.
It was Delhi's second straight win in the tournament following their triumph over Kings XI Punjab [ Images ] in Mohali on Saturday.
Rajasthan, having been beaten by Mumbai Indians [ Images ] on Saturday, suffered a second straight defeat.
Coming into the match per se Delhi witnessed Sehwag going ballistic from the first over. The former captain helped himself to a couple of boundaries each in the opening two overs bowled by Dimitri Mascarenhas [ Images ] and Shaun Tait [ Images ] respectively before going full throttle in the third over (bowled by Munaf Patel [ Images ]).
Munaf's first ball went over the long-off fence and his second reached the mid-on boundary.
Gautam Gambhir [ Images ] (9) also helped himself to a boundary in that over.
However, Mascarenhas struck twice in the fourth over, first having the Gambhir caught at mid-on by Graeme Smith [ Images ] and then having Tillekeratne Dilshan [ Images ] (0) caught by stumper Naman Ojha [ Images ] of the next ball.
It was Dilshan's second successive duck in the tournament.
AB de Villiers [ Images ] survived the hat-trick ball.
And then Sehwag exploded.
The second ball of Mascarenhas's third over (the innings' sixth) cleared the long-off fence, the third was sliced to the point boundary and the fourth was top-edged behind short fine-leg: a sharp chance which Tait failed to latch on to.
And Amit Uniyal's morale suffered a beating in the seventh.
Sehwag cleared the long-off fence again with the first ball and cut the second to the third man boundary -- the shot ensuring his half-century.
It was Sehwag's fifth IPL fifty and also happened to be the fastest ever in the tournament (off just 21 balls).
The Delhi veteran celebrated the occasion by hoisting the third ball for yet another maximum -- his fourth.
It took a strategic time-out and a brilliant catch thereafter for the Rajasthan team to plot a Sehwag dismissal.
Off the last ball of the 10th over by Munaf, Sehwag skied to midwicket and Smith kept his eyes on the ball to take a blinder.
Sehwag's 34-ball knock was inclusive of eight hits to the fence and five massive ones over it.
Three overs later, Shane Warne [ Images ] struck, inviting De Villiers (15) to play a cover drive and substitute Fazal taking an excellent catch at short cover.
Earlier, Delhi Daredevils made most of their decision to bowl first, restricting Rajasthan Royals to a modest total.
Rajasthan Royals could score just 141 for six in their stipulated 20 overs, Abhishek Jhunjhunwala top-scoring with an unbeaten 53, his maiden IPL fifty.
The frailties in Shane Warne's side, the many chinks in their armour, were apparent soon after the commencement of the game, and soon their batting weaknesses lay exposed.
None of their top batsmen got going and the team found itself in the rut right from the beginning.
They compounded their woes and helped Delhi's cause by playing some rash shots. Added to that, poor coordination between their batsmen saw them throw their wickets away in the bargain.
A 60-run fifth wicket partnership between Paras Dogra (29) and Jhunjhunwala was the only bright spot in an otherwise vapid batting display.
Gautam Gambhir, the Delhi captain won the toss and decided to field.
"Hopefully we can restrict them to a total that we can chase," said Gambhir.
His Rajasthan counterpart seemed to agree. "We would have also liked to bowl," said Warne. "The dew factor comes up later and it could be a deciding factor," he added.
Gambhir's decison was vindicated by his bowlers.
Asnodkar (5), who had began with an exquisite boundary off Ferveez Maharoof, was snapped up by Tillekeratne Dilshan at backward point.
In came Naman Ojha (24) and he got going almost immediately, hitting two boundaries in three balls off Maharoof.
The introduction of Amit Mishra [ Images ] to the attack in the fifth over was an invitation for Ojha to go ballistic.
The leg-spinner's second ball was cut past point for a boundary, his third was swept to the square leg boundary and the fourth cleared the long-on fence.
However, Mishra had his revenge with the fifth ball, cleaning up Ojha with a googly.
In came Yusuf Pathan [ Images ] to a roaring reception from his home crowd. However, Yusuf, who had scored a 37-ball hundred against Mumbai Indians on Saturday, was dismissed for a fifth-ball duck.
He failed to pick a slower one from Maharoof and AB de Villiers made no mistake at mid-on.
Graeme Smith (18) didn't last long either. Virender Sehwag juggled, almost dropped, but finally held onto the chance offered by the South African at deep midwicket to give Pradeep Sangwan his first wicket.
Rajasthan were 50 for four at the start of the ninth over.
Dogra and Jhunjhunwala gave the total a semblance of respectability with a fifth-wicket stand.
Dogra was the more aggressive of the two, helping himself to maximums from both Mishra as well as Sarabjit Ladda.
However, he was run-out at a crucial juncture, just when Rajasthan were looking to open up.
Dimitri Mascarenhas (3) ran himself out as well in the next over to compound Rajasthan's woes.
Jhunjhunwala, on his part, played a reticent knock, interspersed with moments of aggression, to ensure the eventual total.
His 45-ball knock was inclusive of five hits to the fence and a huge one (off Ladda) over it.
Amit Uniyal remained unbeaten on four.