The 2012 and 2016 champions, the only nation to win this tournament more than once, are in real danger of crashing out before the Super 12s after being skittled for 118 in pursuit of 161 at a chilly Hobart.
Scotland, who have played just two T20s this year and lost both heavily against New Zealand in late July, were grateful for George Munsey's 66 not out off 53 balls underpinning their 160 for five.
The Windies raced to 53 for one but Evin Lewis was out from the penultimate ball of the powerplay, the start of an alarming collapse that saw them lose seven wickets for 26 runs in 45 deliveries.
They ultimately subsided in 18.3 overs and head coach Simmons had no doubt about where to place the blame after a major upset.
"The only way you can look at it is - disappointed," Simmons said. "Our batting definitely was a bit unprofessional. We need to wake up and start being as professional as we can be when we are batting.
"The bowlers seem to be working hard and putting us in good positions, but the batters continue to falter. Too many soft dismissals. As batsmen you have to pay a bit more attention to your wicket.
"Every time, we play we are up there with the run-rate. But we keep losing wickets and soft wickets. I've been trying to remedy it for the last couple of months. It doesn't seem like it's there yet."
Slow left-armer Mark Watt, so often critical to Scotland's recent success, was skilful as he changed his pace and bowled from various points behind the crease, to collect three for 12 from four overs.
Fellow spinner Michael Leask finished with two for 15 from his four overs to significantly boost Scotland's hopes of reaching the Super 12s for the second year in a row.
Twelve months ago they overcame Bangladesh, Papua New Guinea and tournament co-hosts Oman to top their preliminary group, the first time they had gone past the first round at any World Cup event.
"The main thing to take away from this is the fact that Scotland since the last World Cup, we've only played two games," Watt said.
"We don't get an awful lot of fixtures where we can try things out and it doesn't matter if we're going to lose. Every game we play is a crunch game. It's tough, but that's associate life."
While the Windies are without the likes of Chris Gayle, Dwayne Bravo, Andre Russell, Sunil Narine and Kieron Pollard, at seven in the world T20 rankings, they are eight places ahead of Scotland.
They must now beat Ireland and Zimbabwe in their remaining Group B matches to give themselves the best chance of avoiding an ignominious first-round exit.
Scotland are daring to dream and captain Richie Berrington said: "To get a win like that at a World Cup - it's pretty special to represent your country at a World Cup - it's as big as it gets.
"The belief has always been there that we can put on that performance. It's certainly a big win for us and one we'll enjoy but we know there's still plenty more to play for."