Dilshan, 39, hit three sixes and eight fours as Sri Lanka overpowered Afghanistan’s 153-7 with seven balls to spare in their opening group match at the Eden Gardens stadium in Kolkata.
Afghanistan, the only non-Test team left in the fray, paid the price for some sloppy fielding after an impressive effort with the bat that saw skipper Asghar Stanikzai make a fine 47-ball 62.
Dilshan gave Sri Lanka a flying start, smacking fast bowler Dawlat Zadran for two sixes on the trot, including one that came off his famous ‘Dilscoop’ shot which typically sails over the wicketkeeper’s head.
Off-spinner Mohammad Nabi briefly put the brakes on Sri Lanka by dismissing opener Dinesh Chandimal for 18, before 17-year-old leg-spinner Rashid Khan accounted for Lahiru Thirimanne (six).
Wicket-keeper Mohammad Shahzad then sent back Thisara Perera with a direct throw at the stumps as Sri Lanka slipped to 85-3, but Dilshan held his nerve to ensure a smooth finish for his side in the end.
Earlier, Stanikzai led his side by example while Samiullah Shenwari chipped in with a handy 31 to help Afghanistan recover from a shaky 51-4.
Paceman Thisara Perera picked up 3-33 in an otherwise disappointing show by the Sri Lankan bowlers who let the Afghans off the hook after a promising start.
New Sri Lankan T20 captain Angelo Mathews gave the islanders the key breakthrough by having in-form opener Shahzad caught at mid-on for eight.
Shahzad, who came into the match with a top-score of 61 in the qualifiers, lobbed an easy catch to Dushmantha Chameera as he tried to pull to the legside.
Shahzad’s opening partner Noor Ali Zadran smacked paceman Nuwan Kulasekara for two boundaries in a row before being bowled by Rangana Herath (2-24) for a 23-ball 20.
Afghanistan suffered another blow soon after when Karim Sadiq (zero) nicked one behind off Perera, but Stanikzai steadied the innings with his quickfire knock, his best in Twenty20 internationals.
Stanikzai seemed to clear the ropes easily, twice lofting spinner Milinda Siriwardana into the stands, much to the delight of a small but noisy group of Afghan fans.
The skipper’s counter-attack came to an end when he was caught by wicketkeeper Chandimal off Perera in the 19th over.