The Glasgow 2014 hosts had to beat the North Americans in their final Pool A game after going down bravely in their opener with New Zealand.
An eight-try demolition of Barbados kept Stevie Gemmell's side in the hunt for the last eight and cheered on by a crowd which would have matched an Old Firm encounter for decibels, they finished off the job with a 21-5 win over Canada.
The Scots now face a tough test against South Africa in Sunday's quarter-final, with a semi-final clash against England or Samoa the reward for the winner.
Winger Lee Jones was the Scots' top performer, touching down five times over the three games.
And he claims the passionate Ibrox support have put his side in with a shout of landing a medal.
The Glasgow Warriors sevens specialist said: "The boys are delighted. Honestly, that crowd was just incredible. To have everyone cheering for you, it's an awesome stadium to play in.
"The fans are right on top of you and when you're playing well you can really hear them. It was phenomenal. That's up there with the best atmospheres I've ever played in.
"It was great to get over the line five times. I think we've showed we're capable of beating anyone.
"We're still on track for a medal and that was our aim coming into this.
"To run New Zealand so close has given us massive confidence going into the quarter-final."
Scotland found themselves 17-0 down against the All Blacks but clawed their way back to within three points after the All Blacks had two men sin-binned for cynical attempts to halt their attacks before time ran out.
They then thumped Barbados 56-0 to set up their last-match decider with Canada.
They made the perfect start when Lee Jones squeezed down the left flank to open the scoring with a try converted by skipper Colin Gregor. But when Connor Braid pulled a score back for the visitors, nerves began to waver.
However, Canada made a mess of the restart and handed Richie Vernon the chance to gallop in to re-establish Scottish command.
Mark Bennett then put the seal on the victory when he wriggled clear of the Canadian defence for the Scots' third try late in the second period.