Chris McStay’s early strike was followed up by a David Goodwillie brace either side of the break to give the Bully Wee a commanding 3-0 advantage.
Stenny’s half-time substitutions had a positive impact, but goals from Eddie Ferns and Harry Paton were not enough to ruin Clyde’s day.
Danny Lennon’s side got off to a flying start in the hammering rain as McStay’s 25-yard effort found the top corner despite a hand from Lewis McMinn in the Stenny goal.
Clyde limited their hosts to few chances in the first half, and went further ahead before the half hour mark through Goodwillie.
A mix-up in the Stenhousemuir defence between Michael and Ross Dunlop allowed the striker in, and he prodded neatly past McMinn.
Stenny’s best chance of the first period came in added on time, when Ruaridh Donaldson’s ball in was flicked clear brilliantly but the outstanding Martin McNiff.
Six minutes into the second period Clyde extended their advantage with one of the goals of the season - a bit of individual brilliance from Goodwillie who dummied the ball and left Stenny captain Michael Dunlop on the floor, before rounding McMinn and slotting home.
Stenny pulled one back within five minutes though, through substitute Ferns. Fellow half-time sub Alan Cook did brilliantly down the left and his cross was scuffed by Mark McGuigan before being hammered in by Ferns from close-range.
Stenny were unfortunate not to pull another back when Paton had a close-range effort cleared off the line.
Clyde had keeper Blair Currie to thank for keeping the score at 3-1, denying Cook with a save down low to his left.
Hearts loanee Paton did make it 3-2 on 75 minutes when he received the ball from a corner and bent a curling effort into the bottom right-hand corner.
But it wasn’t enough to stop Clyde taking all three points.