Levi lashed 101 from just 97 balls on the second day of the Specsavers County Championship Division Two clash at Cardiff.
Rob Newton (67) also racked up the runs as Northants took the lead, having bowled Glamorgan out for 207.
But the home side did fight back a bit with the ball as after Levi’s departure at 241 for three, Northants were dismissed for 310.
That meant the lead was 103 and Glamorgan ate into that as they finished the day on 63 for one, with Richard Gleeson, who took five for 60 on the first day, bowling Nick Selman for 13.
But there was no doubt that the day belonged to Levi.
And the South African batsman said: “The last three times I’ve got close I’ve got out in the 90s, so to get over the line was nice.
“Batting at four in the last couple of games has been different but I’ve scored runs so I’m not going to complain.”
“It wasn’t the easiest out there but me and Rob stuck in.
“They started searching a bit so we got a few scoring shots.
“To walk away with a hundred - I’m happy, but I’d rather have batted for another hour and got a big one.
“It’s that kind of wicket - nothing happens for half a session then four or five wickets fall.
“For a new guy coming in, it’s not the easiest.
“We didn’t bowl as well as we should have but I think the guys will have learned and come back with better plans.
“They should not have scored as much as they did this evening, but we just searched a bit.”