Head coach Gautam Gambhir, in his first Test assignment, aims to secure a series win
The home side reached their revised target of 212 runs in 40 overs With 17 balls to spare after rain delayed the start of their innings by nearly two hours.
Bangladesh, who earlier dismissed Sri Lanka for 232, will play Pakistan in the final on Thursday, with five-times champions India out of the tournament despite finishing level on points with Bangladesh.
India paid the price for their shock defeat by Bangladesh which sent them out on the teams’ head-to-head record.
Nuwan Kulasekara claimed two wickets in his opening spell to help Sri Lanka reduce Bangladesh to 40 for three but Tamim and Shakib added 76 runs for the fourth wicket.
Unheralded off-spinner Sachitra Senanayake, playing his first match of the tournament, briefly threatened to spoil Bangladesh’s party when he dismissed both batsmen in the space of four overs.
Tamim gave Senanayake a sharp return catch just after completing his third fifty of the tournament, but the bowler could not grasp it.
Senanayake, however, got his reward for superb bowling when he had Tamim caught by Lahiru Thirimanne for 59 off 57 balls.
Four overs later Shakib fell for 54 to Senanayake, who kept one low and trapped the left-hander lbw.
Nasir Hossain and Mahmudullah continued the Bangladesh momentum, delighting the Sher-e-Bangla crowd which included Bangladesh Prime Minister Sheikh Hasina.
Nasir was unbeaten on 36 and Mahmudullah made 32 not out, the pair adding 77 runs for the sixth wicket.
Earlier fast bowler Nazmul Hossain, playing his first match in the competition, produced a brilliant opening spell which earned him the prized scalps of Mahela Jayawardene (five), Tillakaratne Dilshan (19) and Kumar Sangakkara (six).
Nazmul, who finished with three for 32, was complemented by his opening partner and former skipper Mashrafe Mortaza who gave away just 13 runs in his first spell of six overs.
Chamara Kapugedera (62), Thirimanne (48) and Upul Tharanga (48) boosted Sri Lanka but two wickets each form left-arm spinners Shakib and Abdur Razzak pegged them back.
COMPLETE SCOREBOARD
Sri Lanka:
M. Jayawardene b Nazmul 5
T. Dilshan b Nazmul 19
K. Sangakkara c Nazimuddin b Nazmul 6
C. Kapugedera c Shakib b Razzak 62
L. Thirimanne st Rahim b Razzak 48
U. Tharanga c Rahim b Shahadat 48
F. Maharoof c Rahim b Shakib 3
N. Kulasekara lbw b Shakib 1
S. Senanayake not out 19
L. Malinga b Mortaza 10
S. Lakmal run out 0
Extras (lb3, w8) 11
Total (for all out; 49.5 overs) 232
Fall of wickets: 1-19 (Jayawardene), 2-29 (Sangakkara), 3-32 (Dilshan), 4-120 (Thirimanne), 5-169 (Kapugedera), 6-175 (Maharoof), 7-183 (Kulasekara), 8-204 (Tharanga), 9-230 (Malinga), 10-232 (Lakmal).
Bowling: Mortaza 9.5-1-30-1, Nazmul 8-1-32-3, Shahadat 8-0-51-1 (w2), Razzak 10-0-44-2 (w2), Shakib 10-1-56-2 (w3), Mahmudullah 4-0-16-0 (w1).
Bangladesh (target 212 in 40 overs):
Tamim Iqbal c Thirimanne b Senanayake 59
Mohammad Nazimuddin b Kulasekara 6
Jahurul Islam c Kapugedera b Lakmal 2
Mushfiqur Rahim b Kulasekara 1
Shakib Al Hasan lbw b Senanayake 56
Nasir Hossain not out 36
Mohammad Mahmudullah not out 32
Extras (lb13, w7) 20
Total (for five wickets; 37.1 overs) 212
Fall of wickets: 1-8 (Nazimuddin), 2-39 (Jahurul), 3-40 (Rahim), 4-116 (Tamim), 5-135 (Shakib).
Bowling: Malinga 8-0-29-0 (w3), Kulasekara 6-0-30-2 (w1), Lakmal 7-0-40-1 (w3), Senanayake 8-0-38-2, Maharoof 6-0-46-0, Dilshan 2.1-0-16-0.
Result: Bangladesh win by five wickets (D/L method)
Man of the match: Shakib Al Hasan (BAN)
Toss: Bangladesh
Umpires: Steve Davis (AUS) and Paul Reiffel (AUS)
TV umpire: S. Ravi (IND)
Match referee: David Boon (AUS)
Next match (final): Bangladesh v Pakistan (Thursday)
Head coach Gautam Gambhir, in his first Test assignment, aims to secure a series win
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