It was Gayle's 13th ODI century as he and fellow opener Shivnarine Chanderpaul made light work of the 161 run target set for victory, winning with 13.2 overs to spare.
The result also sealed Sri Lanka's place in the next round as the two countries join Australia, England, India, South Africa, New Zealand and Pakistan.
Brian Lara's team will now clash with Sri Lanka in the last league match on October 14 in Mumbai to decide the qualifying round winners.
"The main thing was to come out with a big win and put some sort of a distance between the two teams. There was a certain difference of class and we showed that," said Lara.
"We lost just one wicket in two games and again it is very good and the confidence of winning will flow in the rest of the team."
The West Indies bowling attack did the damage early with fast bowler Corey Collymore (2-36) and off-spinner Marlon Samuels (2-27) playing key roles in setting up the West Indies victory.
In contrast the Bangladeshi seamers and spinners could never test left-handers Gayle and Chanderpaul.
Gayle was at his swashbuckling best, after he reached his half century he hit three massive sixes, the last landing on the roof of the stand.
"He (Gayle) played each ball on merit and we won by 10 wickets. That's great," said Lara.
Chanderpaul was a valuable foil, hitting six fours in his 104-ball knock.
After electing to bat, Bangladesh started well were strongly placed at 95-1before collapsing as they lost their last nine wickets for just 66 runs.
"It was a bad game for us," said Bangladesh captain Habibul Bashar.
"I feel it was a mixture of good bowling and bad batting for us which is really not acceptable as we were 95-1 at one stage."