Richie Berrington, finished the game with a huge six to remain 31 not out. Matthew Cross (26) was also undefeated.
Scotland will go into Group 2 of the Super 12s alongside Afghanistan, India, New Zealand, Pakistan and the runners-up from qualifying Group A - likely to be either Ireland or Namibia.
“This is an opportunity for Scotland to test themselves against the best,” said Coetzer.
“There’s a real togetherness among our squad, through thick and thin.
“This group we were just in was a mighty tough group so the next one will be tougher. We will go into every game full of hope and belief that we can win more games.”
Bangladesh, who were stunned by Scotland in their opening game, secured the second qualifying spot in Group B by seeing off Papua New Guinea by 84 runs.
They will now play in Group 1 alongside Australia, England, South Africa, West Indies, probably Sri Lanka and either Ireland or Namibia.
“What a day for Scottish cricket, the boys are buzzing,” said man-of-the-match and fast bowler Josh Davey who took 3-25.
Scotland came into the 2021 tournament having never progressed beyond the first round in their three previous appearances, winning just one game in seven.
Scotland restricted Oman to 122 all out.
Oman, who won the toss and opted to bat, had a terrible start when Jatinder Singh was out second ball following a run-out mix-up which left him and opener Aqib Ilyas at the same end.
Ilyas went on to top score with 37 off 35 balls but the home side never shook off the shackles of the Scottish bowling.
Only three Oman batters reached double figures.
“I feel sorry we couldn’t deliver, but we are confident our moment will come,” said Oman skipper Zeeshan Maqsood.
Shakib Al Hasan smashed 46 and had bowling figures of 4-9 as Bangladesh crushed Papua New Guinea.
Chasing 182 for victory, PNG were bowled out for 97 in 19.3 overs to hand Bangladesh their second straight win.
PNG go out of the tournament with three losses.
The Tigers bounced back from an opening loss against Scotland to register two convincing wins and the last one would have been bigger had it not been for Kiplin Doriga’s unbeaten 46.
“Every game we’re playing gives us more confidence. Obviously it was a setback, the first game, but in the T20 format the team that is better on the day wins,” said man-of-the-match Shakib.
Shakib equals Afridi
Shakib, a left-arm spinner, struck twice in his first over and then took two more to equal Pakistan’s Shahid Afridi as the leading wicket-taker with 39 scalps in T20’s showpiece event.
Earlier Skipper Mahmudullah Riyad, who hit 50, and Shakib helped Bangladesh to 181-7 after they elected to bat first.
Afif Hossain’s quickfire 21 and an unbeaten 19 off 6 balls from Mohammad Saifuddin, who finished the innings with two sixes and a four, fired Bangladesh to the highest total of the tournament so far.
On Friday, 2014 champions Sri Lanka meet the Netherlands, who are already eliminated, while Ireland and Namibia clash for the last qualifying place.