"Every time there was a slight mistake, a team-mate was there to bail them out," said head coach David Gray. "It was a massive collective performance.
"It's an incredible run and the players deserve all the credit for it. It's been a huge collective effort."
Levitt's firmly struck early opener squirmed away from Butland, while Boyle's fine breakaway goal - from Jordan Obita's pass - was allowed to stand after the VAR officials confirmed he was onside after bursting from his own half.
Before Hibs' second, substitute Nedim Bajrami thought he had equalised for Rangers but watched a magnificent attempt come crashing back off the bar.
Cyriel Dessers, again, passed up a hat-trick of first-half chances, forcing a good save from Jordan Smith before twice blasting over when well placed.
The striker also seemed certain to score 10 minutes from time but failed to make contact from close range.
It was not the preparation Rangers would have wanted with Athletic Bilbao heading to Ibrox on Europa League duty on Thursday.