Peter MacDonald headed Stirling in front after 11 minutes only for former Aberdeen striker David Goodwillie to level for Clyde shortly before half-time.
Moments after the restart, Mark Burbidge gave Clyde the lead after a long throw caused Albion havoc, but the hosts soon levelled through a Callumn Morrison header. A flash of quality from Goodwillie sealed the points though as his through ball set up Barry Cuddihy to net an 80th minute winner.
Second-placed Montrose move to within a point of the leaders after rescuing a 1-1 draw at Peterhead. Jack Leitch fired Peterhead into a spectacular lead in the 71st minute but a header from Chris Templeman in the final minute salvaged Montrose a point.
Stenhousemuir climb to third courtesy of a hard-earned 1-0 victory over second-bottom Cowdenbeath.
Nathan Blockley struck the winner for the Warriors three minutes before the break after good work from Mark McGuigan.
Elgin City slide to fifth after losing 1-0 to Annan Athletic at Borough Briggs. Rabin Omar was felled by Elgin’s Marc Waters in the 24th minute and the resulting spot-kick was duly converted by Annan’s Aidan Smith. Thomas Reilly missed a late one-on-one for Elgin.
Bottom side Edinburgh City picked up their first points of the campaign with a 1-0 win over Berwick Rangers thanks to a stunning free-kick by Ashley Grimes in the second minute.