Angelo Mathews took the wicket of Watson for 21 in the seventh over, but that brought Karun Nair to the crease and he and Rahane put on a third-wicket partnership of 113 as the Royals finished on 189-2 from their 20 overs.
Rahane finished unbeaten on 91 from just 54 balls, while Nair fell in the penultimate over after bashing 61 off 38.
In reply, Delhi got off to a slow start and never looked like threatening Rajasthan's total until JP Duminy (56) built some middle-order partnerships to give the Daredevils an outside chance.
It wasn't to be, though, as no other Daredevil scored higher than 22, with their innings coming to an end at 175-7.
Rajasthan have as many wins as the Chennai Super Kings, but the latter has two games in hand in the race for first place. Delhi, meanwhile, are one of five sides in mid-table separated by just one point.