The 29-year-old Somerset opener, only the tenth England player to play in 100 one-dayers, faced 76 balls with 16 fours for his ninth One-day International hundred.
His fellow left-hander Andrew Strauss finished on 82 not out off 77 balls with one six and 10 fours as England, chasing 191 for victory, won with 25.1 overs to spare.
It was only the second time in 414 matches that England had won a One-day International by 10 wickets after beating West Indies by the same margin in July 2000 at Chester-le-Street.
As runs flowed, first change Khaled Mahmud saw his opening over go for 21 runs with four fours and three no-balls.
Trescothick, who scored 191 and 154 in England’s 2-0 Test series win against Bangladesh earlier this season, twice cut Mahmud over the head of wicket-keeper Khaled Mashud for cheeky fours.
On 89 he almost holed out against left-arm spinner Mohammad Rafique, the ball dropping short of Tushar Imran, who was slow to run-in from long-on.
All the Bangladesh bowlers suffered, with seamer Nazmul Hossain’s seven overs costing 61 runs.
Even though they set a far from challenging target, Bangladesh were lucky to have made 190 after their collapse to 76 for six having lost the toss.
But Aftab Ahmed (51) and Rafique (30) doubled the score to 152 for seven.
Then tailenders Mashrafe Mortaza (29 not out) and Nazmul put on 31 for the last wicket.
Fast bowler Stephen Harmison took four for 39 while Jon Lewis, on his full ODI debut, claimed three for 32 as he made short work of the Bangladesh top order.
Scoreboard
BANGLADESH:
Javed Omar lbw b Lewis 13
Nafees Iqbal c Jones b Lewis 19
Mohammad Ashraful c Flintoff b Lewis 0
Habibul Bashar c Jones b Harmison 19
Tushar Imran b Harmison 10
Aftab Ahmed run out 51
Khaled Mashud c Jones b Harmison 1
Mohammad Rafique c Harmison b Gough 30
Mashrafe Mortaza not out 29
Khaled Mahmud c Pietersen b Harmison 0
Nazmul Hossain c Jones b Gough 6
EXTRAS (LB-4, W-4, NB-4) 12
TOTAL (all out, 45.2 overs) 190
FALL OF WKTS: 1-19, 2-19, 3-39, 4-57, 5-72, 6-76, 7-152, 8-159, 9-159.
BOWLING: Gough 8.2-0-33-2 (3nb); Lewis 10-0-32-3 (1w); Harmison 10-0-39-4 (1nb, 2w); Collingwood 8-0-36-0; Flintoff 9-2-46-0 (1w).
ENGLAND:
M.E. Trescothick not out 100
A.J. Strauss not out 82
EXTRAS (LB-5, W-1, NB-4) 10
TOTAL (for no wkt, 24.5 overs) 192
DID NOT BAT: M.P. Vaughan, V.S. Solanki, P.D. Collingwood, A. Flintoff, K.P. Pietersen, G.O. Jones, J. Lewis, D. Gough, S.J. Harmison.
BOWLING: Mashrafe Mortaza 6-1-33-0; Nazmul Hossain 7-0-61-0 (1nb, 1w); Khaled Mahmud 3-0-39-0 (3nb); Mohammad Rafique 6-0-40-0; Aftab Ahmed 2.5-0-14-0.
UMPIRES: M.R. Benson (England) and Aleem Dar (Pakistan).
TV UMPIRE: N.J. Llong (England).
MATCH REFEREE: J.J. Crowe (New Zealand).
MAN-OF-THE-MATCH: Marcus Trescothick.
NEXT MATCH: Australia v Bangladesh at Cardiff on Saturday.—Agencies