Spinner Wanindu Hasaranga (3-13) led Sri Lanka's disciplined bowling as the Asia champions restricted Afghanistan to a modest 144-8 in the Group 1 contest at Gabba.
Dhananjaya de Silva smashed an unbeaten 64 to help the 2014 champions prevail with nine balls to spare and revive their campaign after back-to-back defeats by Australia and New Zealand.
Sri Lanka now have four points from as many matches, while Afghanistan stay rooted at the bottom with two.
"Last 10 days, we didn't play a game, so we did not get any momentum in the tournament," Afghan captain Mohammad Nabi said referring to their washed-out matches against New Zealand and Ireland.
"We have one more game and hopefully we do well."
Electing to bat, Afghanistan were subdued in the powerplay and were 68-1 at the halfway stage of their innings.
Rahmanullah Gurbaz (28), Usman Ghani (27) and Ibrahim Zadran (22) could not convert their starts and Hasaranga denied them any late flourish.
Hasaranga, the tournament's most successful bowler with 13 wickets from seven matches, also won his duel with Rashid Khan whom he bowled for nine.
Rashid, who left the field with a knee injury just before de Silva sealed Sri Lanka's victory, claimed 2-31 but Afghanistan remained winless in the Super 12 stage.
