The home side resumed with a mountain to climb at 156-8 in their first innings, and although George Garrett edged Fernando over the slips, the tail-ender dominated the early scoring in a stand of 54.
They lasted 52 minutes before Garrett, on 35, edged Zain Ul Hassan behind, and the seamer then bowled Kashif Ali for three leaving former Warwickshire wicketkeeper Benjamin frustratingly stranded six short of a first ton for his new county.
Harry Finch and Ben Compton defended quietly until lunch but after the break Finch hit the first three balls from Ul Hassan for four, only to lose partner Compton lbw to Fernando for 17.
Kent’s top order fell apart for the second time in the game as Daniel Bell-Drummond edged Andy Gorvin to a diving Kiran Carlson at slip and Finch (28) edged Fernando through to Chris Cooke.
A bizarre interruption saw most of the players and umpires hit the deck briefly as a bee swarm was sighted, not helping Jack Leaning’s concentration as he was caught behind off Fernando next ball.
Ekansh Singh, 18, was on a pair but squirted one past short-leg to get off the mark to knowledgeable applause from the Kent faithful, managing one boundary before providing Cooke with another catch off van der Gugten.
The Netherlands international then disposed of Benjamin and Grant Stewart before top scorer Muyeye was trapped lbw by James Harris and Matt Parkinson hammered a return catch to batting hero Ben Kellaway.
As the afternoon session was extended, a slightly farcical end saw the visitors turn to double spin to improve their over-rate and last man Kashif slammed Kiran Carlson for three sixes.
He holed out to Gorvin on the mid-wicket boundary off Kellaway for 32 and that was that with four sessions to spare.
Kent travel to Gloucestershire on Friday 16 May while Glamorgan host Northants, with Australian star Marnus Labuschagne replacing Colin Ingram for two weeks.
Glamorgan’s Timm van der Gugten told BBC Sport Wales:
“We probably didn’t think it was going to happen that quickly, but very happy that it did, and it was a pretty complete performance.
“It’s probably the biggest win I’ve had anywhere in my career, set up by the batters, then as a collective I thought we bowled really well, kept it simple, kept the stumps in play, stifled their runs and took the wickets where we could.
Coach Richard Dawson added:
“A very good effort by the lads, last week we played some good cricket against Derbyshire but didn’t get over the line so to back it up and play the way we did was really pleasing.
“Over the last few weeks we’ve talked about playing on the front foot in the first innings.
“Ben got the big score, Asa (Tribe) played really well again. They’ve got talent, they work hard, they’re keen, and they’re eager for runs and they’ve got ability so it’s been good to see them put together performances, under pressure after being put in.”