Steve McCormack’s men came from behind to do all they could at Salford, but it will be all in vain should the Italians beat Tonga in Halifax.
It took until after the break for them to recover from the loss of Ben Fisher in the warm-up, the former London hooker cruelly having his career ended by a calf injury at his swansong tournament.
He was replaced in the starting line-up by Andrew Henderson, who got through a mountain of work especially in the first half, but it was the decision to move Danny Addy in to the dummy half role in the second half that got Scotland moving.
They scored four second-half tries to recover from a 8-0 half-time deficit, including three in an 11 minute purple patch.
They must now hope that Tonga can do them a favour on Sunday, or they face being eliminated despite earning five points and going through the group stages unbeaten.
For USA, half-backs Joseph Paulo and Craig Priestly once again impressed, as the Tomahawks got through their third game in nine days, and will enjoy a well deserved break until their quarter-final against Australia on Saturday week.
USA claimed their second try through some Priestly mastery. Field position had been granted following a bizarre incident that saw Tui Samoa lash the ball at Dale Ferguson following an apparent crusher tackler, and Priestly dabbed the ball in goal early in the tackle count, with centre Taylor Welch beating the dead ball line to touch down.
For the rest of the first half, Scotland huffed and puffed, and they thought they’d scored when Brough dummy and darted through to jump under the sticks, only to be brought back for a slightly harsh obstruction.
Needing a win to keep their quarter-final hopes alive, Scotland came out firing second hal;f, and they got on the board on 52 minutes.
With Addy now running the game at dummy half, Scotland made it a quick-fire double, as the impressive Matty Russell jinked in off his right foot to score, and Brough’s conversion nudged USA ahead at 10-8.
It was a lead they never looked like squandering, and Hurst was once again denied a try, his elbow hitting the touchline as he dived over from dummy half.
Hard-working prop Douglas, who qualifies through a grandfather, powered over the line after USA were pegged for offside.
And Scotland added a fourth on the hooter, as winger Hurst got a try that his performance deserved, taking Brough’s long pass to secure the win.
Scotland: Russell, Hurst, Hellewell, Addy, Scott, Brough, Wallace, A Walker, Henderson, Douglas, B Phillips, Ferguson, Kavanagh. Interchanges: Barlow, Szostak, Stringer, Wilkes.
Venue: AJ Bell Stadium, Salford