Wicketkeeper Niall O’Brien played the outstanding innings with a hard-hit 93 as Leicestershire moved to 297-6, just 51 runs behind Glamorgan at the SSE Swalec Stadium.
O’Brien fell to Graham Wagg with the new ball, before bad light ended play.
Opener Paul Horton made a measured 67 on day two, in his first Championship knock for the Foxes.
David Lloyd claimed two victims while Timm van der Gugten took his first wicket for Glamorgan.
Glamorgan batsman Chris Cooke was presented with his county cap in the tea interval, in his fourth season with the club.
Glamorgan bowler Timm van der Gugten told BBC Wales Sport: “As a team we bowled pretty well in stages and then let the game get away from us a little bit at times, but if we rock up in the morning and get early wickets, the game will be right back on.
“It was quite hard out there, it’s a nice batting wicket so you have to work hard for your wickets.
Niall (O’Brien) batted really well so it was good to get him out with the new ball.
“I think the morning session will be the vital one and whoever wins that will be in control, so hopefully we can get on top.
“It was a great feeling (to be told I was playing) and I’m very proud to represent Glamorgan, hopefully I can do it for years to come.”
Leicestershire wicketkeeper Niall O’Brien told BBC Sport: “It’s only the second time in my career I’ve been out in the nineties, so I’m a bit disappointed not to have gone on, but in the context of the game it’s put us in a decent position.
“There’s a lot of work to do in the morning, but it’s not a bad pitch, and the lower order can build us a first innings lead and put us in a decent position.
“Wayne White is into the 40s, and if we can get a 40 or 50 run lead it would be very handy.
“Runs second time around might not be so easy, with the bounce beginning to get a bit variable, so it’ll be a big first session tomorrow.”