Afghanistan captain Rashid Khan hailed the inspiration of cricket legend Brian Lara for helping them secure a place in the T20 World Cup for the first time.

Afghanistan reached the last four for the first time courtesy of a knife-edge, eight-run victory over Bangladesh on Monday, a win that also saw mighty Australia eliminated.

"I think we have proved one person right was Brian Lara, the only person who mentioned Afghanistan will be in the semis," said Rashid.

"I think we told him that when we met him in the welcome party. When you get that kind of great, great statement from a legend, as a team, I think it gives you lots of energy."

Afghanistan will face undefeated South Africa in the first semi-final in Trinidad on Wednesday.

India will tackle defending champions England in the second semi-final in Guyana on Thursday.

Defending a modest total of 115-5 against Bangladesh in their final second round Super Eights match on a bowler-friendly surface, Rashid finished with figures of 4-23.

Naveen-ul-Haq took 4-26 as Bangladesh were dismissed for just 105, chasing a revised target of 114 off 19 overs.

On a night of fluctuating emotions there were also three rain delays which saw various mathematical equations come into play.

Had Bangladesh scored their runs in 12.1 overs, they would have won the match and claimed the remaining semi-final spot.

There was tension after Bangladesh fell behind the asking rate at the end of the 11th over when Afghanistan all-rounder Gulbadin Naib went down with cramps just as the threat of more rain appeared.

Rashid insisted the incident was not a device to keep his side ahead of the run rate should the match be halted permanently.

"He had some cramp, I don't know what happened to him and I don't know what's going on in social media but that doesn't matter," said the captain.

"It's just a field injury which comes and then we haven't lost any overs, the rain came and we just went off, it's not something like brought a massive difference in the game.

"We came back on field after five minutes and there was no massive difference. For me, it's just like a small injury, you have to take some time."

South Africa made the semi-finals with seven wins in seven matches but they have been pushed to the limit.

Against Nepal in the opening round, they won by just one run.

However, South Africa have defeated Afghanistan in their only two other T20 meetings -- by 59 runs at Barbados in the 2010 World Cup and 37 runs in Mumbai six years later.

"It's a big achievement for us as a team and a nation being in the semi-finals and with the cricket we have played in the whole tournament I think we deserve it," added Rashid who played in that 2016 defeat, where he went wicketless for 51 runs.