Chris Gayle (48) seldom allows his partner to dominate a stand but Smith did just that in their 97-run opening partnership to help the holders to a commanding 171 for seven at the Sher-e-Bangla National Stadium.
Bangladesh made four changes to the playing XI that lost to Hong Kong in the qualifiers but still folded for 98 in 19.1 overs as West Indies bounced back after Sunday's defeat against India to boost their semi-final hopes.
Paceman Krishmar Santokie's (3-17) early double strikes reduced the hosts to 16 for three in the fourth over and leg-spinner Samuel Badree (4-15) then claimed three wickets in one over to leave the hosts floundering.
"We were confident and this win will make us even more confident. I think we are back on track," Smith, adjudged man-of-the-match, told reporters.
Earlier, Gayle looked uncharacteristically subdued, preserving his aggression for a late assault that eventually did not materialise.
Smith was fluent at the other end, hitting off-spinner Sohag Gazi for four successive boundaries to bring up his half-century.
"I'm not worried about outscoring Chris. I'm just there to get partnership and get West Indies in a strong position," said the free-scoring right-hander.
Even his top edge cleared the mid-wicket boundary for his third six before Smith fell in the next ball to off spinner Mahmudullah, attempting a similar shot.
Gayle, then on 19 off 27 balls, went on to hit Shakib Al Hasan for a six and four in the same over but fell to a superb catch after a run-a-ball knock.
Tamim Iqbal took the catch on the boundary line and lobbed the ball as his momentum took him over the rope before returning to complete the catch.
The fielder took another stunning catch at short third man, leaping to his right to land with a one-handed blinder to dismiss the scoreless Dwayne Bravo in contrast to otherwise a sloppy fielding display by his team.
"Our bowling was OK but our fielding was not. We dropped a couple of catches and also conceded cheap boundaries. I think we gave away 20 more runs with our (poor) fielding," rued Bangladesh captain Mushfiqur Rahim who topscored for the hosts with 22.
West Indies had the perfect platform to launch a late assault to further swell the tally but they lost wickets in a heap towards the end, including four in the last over, to fall short of the 175-mark.
- Sports & Recreation
- Chris Gayle