Daniel Bell-Drummond made a hard-hit 84 while there were brutal innings from Darren Stevens and Mitch Claydon, as five batsmen passed fifty.
Michael Hogan with 4-91 and Craig Meschede, who took 3-105, were the pick of an inconsistent Glamorgan attack.
Stevens completed the visitors' misery by removing captain Jacques Rudolph.
Kent's Daniel Bell-Drummond told BBC Radio Kent:
"It was a brilliant day for the team as a whole. No-one got that big score, but everyone got a start and contributed to the team to post near enough 500. A brilliant team effort.
"If partnerships come for Glamorgan now, we have to sit in and trust ourselves that the wickets will come. Hopefully we'll bowl them out short of the 228 lead but, if we don't, we need to back ourselves to get the runs.
"We've got to be ruthless and try and go for the kill now, but they're a good team and, if they come back hard, it's no dramas. As long as we win, we'll be happy."
Glamorgan fast bowler Michael Hogan told BBC Wales Sport:
"We're behind the eight-ball a little, or a lot to be fair. We probably shot ourselves in the foot on the first day with the way we bowled.
"Claydon is a dangerous player. You can't have fielders everywhere when you're behind in the game. These guys have a licence to tee off - that's the way the game goes.
"My personal efforts don't mean much. It's nice to get a few wickets but you would trade it for them being bowled out for two hundred less. It's a difficult task but we won't shirk it. It's time for us to show what we're about as a team."
Kent's batsmen smashed their team into a winning position on a whirlwind day of action at Canterbury, after taking a massive first-innings lead of 228 runs.