Before the rain halted the game for almost three hours, the Lankans faced the wrath of the Afghan bowling attack. They lost 7 wickets in a gap of 36 runs while posted a paltry 201 after the rain stopped and the game was reduced to 41-overs aside.
Afghanistan needed a rain-revised target of just 187 from 41 overs. After a decent start, they slipped to 54-5 in their chase but a partnership of 64 by Najibullah Zadran and captain Gulbadin Naib gave them hope.
Nuwan Pradeep returned and took two quick wickets before Najibullah was run out by Dimuth Karunaratne for 43.
That left the final pair needing 42 more to win but Lasith Malinga bowled Hamid Hassan with a trademark yorker four balls later.
Victory would have been Afghanistan's second at a World Cup and first against a Test-playing nation at the tournament. Instead, Sri Lanka earn their first win of the marquee event.
Earlier, the Sri Lankan middle-order failed to convert it into a good total as Afghanistan off-spinner Mohammad Nabi rattled their top-order to restrict them to 201 runs in the rain-affected match at the Sophia Gardens, here on Tuesday.
Rain played spoilsport in the clash as the contest was reduced to 41 overs and Afghanistan were handed a revised 187-run target.
Opener Kusal Perera was the lone fighter and top scorer for his side with a valiant 78 runs off 81 balls, while all other his teammates succumbed before the minnows' bowling attack.
Put into bat, Dimuth Karunaratne (30 off 45) and Perera took the island nation to a flying start as the duo steadily took their side near the three-digit mark. However, when Sri Lanka were at 92 runs, the whole scenario changed as Karunaratne while trying to clear the boundary, mistimed Nabi's delivery and ended up handing a catch to Najibullah Zadran at long-on in the 14th over.
Perera and Lahiru Thirimanne (25 off 34) were then involved in a short 52-run partnership for the second wicket. However, the latter's stay was cut short by Rashid Khan in the 22nd over.