Taking a one-goal lead into the second leg at Balmoor, the Blue Toon scored three unanswered goals to keep alive hopes of a swift return to Scotland’s third tier.
Mason Robertson, the matchwinner at Forthbank in midweek, headed them in front six minutes before the break and then Rory McAllister and Jason Brown killed off Stirling’s chances with smart finishes in an eight-minute period early in the second half.
McInally, whose side will face Stenhousemuir in a make-or-break double-header, said: “We were worthy winners after coming through the first 15 minutes.
“Stirling started quickly, got us turning, and put us under pressure, but once we settled down we started passing the ball well and looked a lot better.
“It was a great goal from Mason which took the pressure off and from there we never looked back. We played some good stuff and were thoroughly professional.”