Second-half goals from Andrew Rose, Danny Johnson and Conor Sammon overturned a wonderful David Goodwillie opener to ensure Well leapfrogged Queen of the South into first place in Group G.
Despite losing midfielder Carl McHugh to injury early on, Motherwell dominated possession and went close in the 15th minute as Elliot Frear cut in from the left and tested Clyde keeper Kieran Hughes.
Sammon glanced a header wide moments later, before the hosts took an unlikely lead just after the half-hour mark through Goodwillie’s third goal of the season.
The former Dundee United striker timed his run perfectly to stay onside before twisting and turning his way past a hapless Peter Hartley and curling the ball into to the bottom corner.
Clyde should have doubled their lead after the restart, Goodwillie again in the thick of it as he brushed Cedric Kipre aside 20 yards out, only to try and find the net himself - with teammate Chris McStay screaming for a tap-in.
And the home side were made to pay as Well hit two goals in quick succession to take the lead.
Frear - Well’s most dangerous player throughout - whipped in a stinging corner that Clyde failed to clear, allowing Rose to help the ball over the line from close range.
Two minutes later, the English winger picked out Johnson, who fired the ball into the roof of the net for his first Motherwell goal since joining from Gateshead.
Sammon struck the third in the final minute, diverting the ball past Hughes from yet another fine cross from Frear.