After Capitals captain Rishabh Pant won the toss and elected to field, 22-year-old Parag aided the hosts in recovering from 36/3 to set the visitors a target of 186.
Royals' bowling attack was efficient in halting the visitors' chase ,and were well in control when Capitals needed 60 from 24 balls.
Tristan Stubbs (44 not out) came out aggressively with the bat and gave his side hope of a first victory of the 2024 season, as Capitals required 17 from the final six deliveries.
But Royals pace bowler Avesh Khan produced a sublime final over, perfectly finding the spot with his yorkers to concede just four runs and wrap up a second consecutive win for the hosts, while condemning Capitals to a 0-2 record.