Nabi's fireworks saw Afghanistan recover from 40-4 to compile a respectable 164-6 after which Rahman's bowling helped to dismiss Bangladesh for 139 in 19.5 overs.
Zimbabwe posted 144-5 and looked headed for victory with Bangladesh 60-6 in the 10th over before the 19-year-old counterattacked in style.
The Border Guard Bangladesh (BGB) completed the task with its own fund on the instructions of Prime Minister Sheikh Hasina.
Bangladesh all-rounder Shakib Al Hasan has reiterated his wish to leave captaincy but added that he understands why he needs to carry on in the role.
Mehidy Hasan had a poor outing in the ODI series in Sri Lanka, which Bangladesh lost 0-3. In the three matches he played in that series, Hasan could scalp only two wickets.
Afghanistan skipper Rashid Khan led the side to a historic Test win over Bangladesh, and created a new record with his figures in the game.
Rashid Khan starred for Afghanistan in the second innings as he led the side to its second Test victory in Chattogram against Bangladesh.
If rain doesn't play spoilsport on the final day of the one-off Test, Afghanistan can register their first-ever Test match victory against Bangladesh in Chittagong.
Mohammad Nabi has played an important role in the rise of Afghanistan cricket at the world stage in recent years, featuring in the country' first-ever Test, T20I and ODI.
17-year-old Ibrahim Zadran and Asghar Afghan shined for Afghanistan on Day 3 as the visitors take command over Bangladesh in the one-off Test.
Rashid Khan took four wickets as Bangladesh find themselves in a spot of bother at the end of the second day, as the hosts trail by 148 runs with just two wickets remaining.
Bangladesh first bowled Ireland out for 85 in 20 overs and then chased down the target of 86 with nine balls to spare in the first semi-final of the Women's T20 World Cup Qualifiers.
Bangladesh, playing without a proper seamer, removed openers Ihsanullah (9) and Ibrahim Zadran (21) early with left-arm spinner Taijul Islam snaring both the wickets.
Rahmat Shah had previously scored 98 in Afghanistan's last Test against Ireland in Dehradun.
Rashid Khan broke a 15-year-old record, which was earlier created by Zimbabwe wicketkeeper-batsman Tatenda Taibu in 2004.
The bomb was thrown from the footbridge at the Science Lab intersection Saturday night when the minister was passing through the area, the Daily Star reported, quoting police and eyewitnesses.
"Names of many Indian citizens who migrated from Bangladesh as refugees prior to 1971 have not been included in the NRC because authorities refused to accept refugee certificates," Sarma said in the micro blogging site.
The Pakistan Cricket Board (PCB) has confirmed that Bangladesh women's cricket team will tour the country for T20I and ODI series in October-November.
The Bangladeshis, all residents of Thakurgaon district of the neighbouring country, claimed that they have been eking out a living at Kulgam in Jammu and Kashmir and they arrived Kishanganj on Wednesday evening, BSF DIG Amritlal Tirkey said.
Hossain operated out of Monterrey, Mexico, where he housed aliens before sending them on the last leg of the journey to the United States.
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