Axar Patel starred with bat and ball to help Delhi recover from 62 for 5 after eight overs, before picking up the key wickets of Mayank Agarwal and Aiden Markram in an economical spell.
Hyderabad: Delhi Capitals 144-9, Sunrisers Hyderabad 137-6 - Delhi Capitals win by seven runs
This season's bottom two teams in the Indian Premier League played out an appropriately tense affair as Axar Patel's all-round performance clinched a crucial win for Delhi Capitals.
Patel, the India left-arm spinner, made 34 at a run-a-ball to help Delhi recover from 62 for 5 after eight overs, before picking up the key wickets of Mayank Agarwal and Aiden Markram in an economical spell.
Manish Pandey also made 34 but was run out by Washington Sundar as Capitals' innings was characterised by a failure to convert starts, with Mitch Marsh and David Warner falling respectively for 25 and 21 either side of Phil Salt's first-ball dismissal.
Sundar was the most successful of Sunrisers' bowlers, claiming 3 for 28 from his four overs, while Bhuvneshwar Kumar was at his skilful, frugal best in accounting for Salt and Patel in his four-over allocation of 2 for 11.
Harry Brook fell cheaply for Sunrisers (Noah Seelam/AFP via Getty Images)
But despite restricting Delhi to just 144 for 9, Hyderabad fell short yet again despite Agarwal's 49 and a quickfire 31 from Heinrich Klaasen.
Harry Brook made just seven off 14 balls, however, and none of Rahul Tripathi, Abhishek Sharma nor Markram could take on the mantle after Agarwal departed for 49 in the twelfth over.
Klaasen, together with Sundar, looked like he might steer them home, but he fell to countryman Anrich Nortje in the penultimate over as his side ended seven runs short of victory, thanks to a terrific final over from Impact Player Mukesh Kumar, whose Capitals franchise have now won their last two games.