After finding themselves behind early in the contest from the penalty spot, the young Gers headed into the interval ahead thanks to a Brian Kinnear own goal and a terrific strike from Josh Gentles.
However, the League Two side levelled with 17 minutes remaining before Kyle Fleming found the top corner from 25 yards out with one of the final acts of the contest to condemn Rangers to defeat.
The strength of Clyde’s lineup certainly reflected their ambitions in this competition, with head coach Liam Ross in the Gers dugout grateful to call upon the likes of Calum Adamson, Callum Burnside, Lewis Stewart, Josh Gentles and Jack Wyllie, all of whom are currently enjoying loans in the lower leagues of Scottish football.
And it was the home side who were on the front foot early through the dynamic Burnside and Stewart on the left-hand side, with the duo combining before the former lashed a thunderous effort that Kinnear was equal to at his near post.
For all of Rangers’ early pressure, though, it was the visitors who struck first when goalkeeper Rydnn McGuire was caught in possession, and he brought down Scott Williamson, who got his toe in front of the teenager and went tumbling over.
The Clyde forward grabbed the ball and dispatched it in off the underside of the crossbar to give the away side an advantage against the run of play.
There was no time for wounds to be licked as Rangers immediately got back on the front foot and went close through Stewart, who had the better of his marker time and time again in the opening period.
The leveller then arrived in fortuitous circumstances when the hosts won a corner, and Burnside’s lofted delivery was inexplicably punched into his own net by Kinnear as he attempted to claw the ball to safety.
Rangers didn’t care, and Zebedee Lawson almost completed a quick turnaround when he danced his way through a crowd of Clyde bodies and shot inches wide.
Ross’ side turned the game on its head just shy of the half-hour mark, and it was a fantastic strike from Gentles.
The 18-year-old received a pass 25 yards out from goal and was presented with the time and space to shift the ball onto his favoured right side, setting his strike around the defender and watching the ball whip ferociously into the far corner.
Lawson went close once again before the interval, this time on his right foot, as the Gers truly looked in the mood for more.
The away side turned to their substitutes bench with a triple substitution at the interval as Gentles went close to doubling his tally on the evening, were it not for the intervention of Kinnear, eager to make amends for his earlier error.
However, Clyde were certainly upping the ante, with Rangers indebted to a wonderful reaction save from McGuire from close range.
Marley Redfearn then spurned wide from close range for the visitors, before McGuire was again called upon as the League Two outfit smelled an equaliser.
The leveller arrived with just over a quarter of an hour to play as Redfearn danced inside from the left-hand side before feeding Darren Hynes on the opposite flank whose stood up delivery was met first-time by Robbie Leitch racing into the penalty box.
It set up a grandstand finish – with a bonus point penalty shootout on offer if the game remained level – as both teams attacked with vigour.
However, for all of McGuire’s second-half heroics, he was helpless in stoppage time when a bouncing ball in midfield broke to Fleming, and the midfielder arrowed an unstoppable effort into the top corner from 30 yards out.
There was still time for the Gers to break forward in stoppage time as Burnside did ever so well to fashion a strike from the edge of the penalty area, which looked destined for the top corner were it not for the intervention of Kinnear at full-stretch to preserve all three points for his side.
RANGERS: McGuire, Hutton, Wyllie (Owen, 85), Hynd, Scally, Adamson, Burnside, Smith, Lawson, Stewart (Fernie, 80), Gentles (Condy, 70)
Subs not used: S. Reid, J. Reid, Young, Cameron
CLYDE: Kinnear, Lyon, Campbell, Cuddihy, Leitch, Williamson, Redfern, Dunachie, Niang, Nevans, Lyon
Subs: Hogarth, Robson, Howie, Hynes, Connell, Fleming, Sutherland, Murdoch
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