Mujeeb had made the previous record in 26 balls against Pakistan in Sri Lanka last month.
Nabi was holed out by Mahesh Thikshana in the 27th over, but Shahidi and Karim Janat (22) kept up the pace and added 33 runs before they were both dismissed in the same over by Velez.
Despite the double blow, Afghanistan did not give up and Najibullah Zadran (23) and Rashid (27 not out) kept them in the contest.
But in a dramatic ending, the Afghan camp did not realize their hopes were still alive after Mujeeb was dismissed and Sri Lanka progressed.
Sri Lankan skipper Dasun Shanaka admitted Nabi almost took away the game.
“It is tough,” said Shanaka, whose team has now won 12 ODIs in a row. “The first target was a game of 37.1 overs and Nabi almost took the game away from us but we got wickets when we needed them.”
Shahidi said: “It is very disappointing to lose. We fought well and gave our best, I am proud of the team, the way they played and fought till the last ball.
