Bangladesh now have two concussion replacements. Mehidy can only bat as he replaced a batsman while Taijul can bowl for the same reason.
Captain Rashid Khan smashed his maiden Test half-century as Afghanistan were bowled out for 342 runs.
Bangladesh fielded an all-spin attack without picking a single pace bowler while Afghanistan handed a Test debut to Ibrahim, Qais Ahmed and Zahir Khan.
Shakib got there in 28 Tests, whereas Taijul did it in his 25th appearance.
Sri Lanka replaced pacer Lasith Malinga, who retired from ODIs after the first game of the series, with Isuru Udana and left out Thisara Perera
The Sixers have won their second match on the trot and are still alive in the tournament.
Taijul returned with impressive figures of three for 10 in his allotted four overs, while Junaid went for 26 runs in his 3.5 overs.
It was Bangladesh's first Test series win in four years, after they won the opener in Chittagong by 64 runs.
Bangladesh avenged their away first Test defeat to the Windies this after they were bowled out for 43 in the first Test, the lowest Test
Mehidy surpassed his own record for the best bowling figures for Bangladesh to achieve career best 12/117.
Bangladesh have two Tests wins in 2017 and will eye drawing level with a third for their best year since 2014.
One wicket in Sri Lanka saw James Anderson slip to second place and put Kagiso Rabada at No 1.
Chasing a target of 204 runs in Chittagong, West Indies stuttered from the start and were all out for 139 on day three.
Taijul Islam claimed six of the 15 wickets that fell on day three of the Chittagong Test.
West Indies lost three wickets for no addition to their total as Shakib Al Hasan and Taijul Islam made inroads.
IND 62/2 OVERS: 26.0
AUS 369 (115.2 Ovs)
IND trail by 307 runs
Sri Lanka vs England - 1st Test
SL 156/2 OVERS: 61.0
ENG 421 (117.1 Ovs)
SL trail by 130 runs
United Arab Emirates vs Ireland - 4th ODI
United Arab Emirates
Match Postponed
Bangladesh vs West Indies - 1st Test
03 Feb, 2021 09:30 IST
Zahur Ahmed Chowdhury Stadium, Chattogram
Sri Lanka vs England - 2nd Test
22 Jan, 2021 10:00 IST
Galle International Stadium, Galle
Pakistan vs South Africa - 1st Test
26 Jan, 2021 10:30 IST
National Stadium, Karachi
Pakistan vs South Africa - 2nd Test
04 Feb, 2021 10:30 IST
Rawalpindi Cricket Stadium, Rawalpindi
Afghanistan vs Ireland - 1st ODI
21 Jan, 2021 11:00 IST
Sheikh Zayed Stadium, Abu Dhabi
Afghanistan vs Ireland - 2nd ODI
24 Jan, 2021 11:00 IST
Sheikh Zayed Stadium, Abu Dhabi
Afghanistan vs Ireland - 3rd ODI
26 Jan, 2021 11:00 IST
Sheikh Zayed Stadium, Abu Dhabi
Bangladesh vs West Indies - 1st ODI
20 Jan, 2021 11:00 IST
Shere Bangla National Stadium, Mirpur
Bangladesh vs West Indies - 2nd ODI
22 Jan, 2021 11:00 IST
Shere Bangla National Stadium, Mirpur
Bangladesh vs West Indies - 3rd ODI
25 Jan, 2021 11:00 IST
Zahur Ahmed Chowdhury Stadium, Chattogram
United Arab Emirates vs Ireland - 2nd ODI
20 Jan, 2021 11:00 IST
Sheikh Zayed Stadium, Abu Dhabi
United Arab Emirates vs Ireland - 3rd ODI
30 Jan, 2021 11:00 IST
Sheikh Zayed Stadium, Abu Dhabi
Sri Lanka vs England - 2nd Test
22 Jan, 2021 10:00 IST | 04:30 GMT
Galle International Stadium, Galle
Australia drew with India
South Africa vs Sri Lanka - 2nd Test
South Africa beat Sri Lanka by 10 wickets
New Zealand vs Pakistan - 2nd Test
New Zealand beat Pakistan by an innings and 176 runs
India beat Australia by 8 wickets
South Africa vs Sri Lanka - 1st Test
South Africa beat Sri Lanka by an innings and 45 runs