Australia has been knocked out of the Twenty20 World Cup after Afghanistan progressed to the semifinals for the first time with a dramatic, rain-hit win over Bangladesh.

Afghanistan only needed to win to advance to the semis, but Bangladesh needed to win with an enormous boost to its net run rate to surpass Australia.

After restricting Afghanistan to 5-115, Bangladesh needed to chase down 116 in 12.1 overs to qualify for the semifinals but the middle order was torn apart by leg-spinner Rashid Khan, who took 4-23 from his four overs.

The target was reduced to 114 by rain and Bangladesh opener Litton Das looked set to carry his team to its first World Cup semi but he was left stranded on 54 off 49 as the last two wickets fell in the penultimate over.

Seamer Naveen-ul-Haq was named player of the match after he finished the job under intense pressure, taking the wickets of Taskin Ahmed and Mustafizur Rahman with the last two balls of the game to finish with 4-26 and send his country into the final four of a World Cup for the first time.

"We have worked so hard over the past few years," Naveen said.

"We were dreaming and working for this day. When [that day comes] it's a surreal experience. I'm lost for words."

Afghanistan leapfrogged Australia for second place in Group 1 of the Super Eights, with unbeaten India topping the group.

India will play a blockbuster semifinal against England in Guyana, while Afghanistan will take on South Africa in Trinidad and Tobago for a spot in the final.

"It's something like a dream for us as a team," captain Rashid said.

"It's unbelievable. I don't have any words to describe my feelings.

"I'm sure it's going to be a massive celebration back home. The country will be very proud."