Ackerman hit 39 fours and a six in a 446-ball knock that helped the visitors to 560 at Sophia Gardens.
Brendon McCullum was 80 not out as Glamorgan reached 153 for two in reply.
In Division One, Murray Goodwin and Matt Prior smashed twin centuries to bat Sussex into a strong position in their crucial clash with Kent.
Former Zimbabwe batsman Goodwin was unbeaten on 111 with Prior 107no at the close at Hove, giving Sussex a lead of 431 on 368 for three.
Carl Hopkinson (57) and Richard Montgomerie (69) weighed in with half-centuries as Sussex, eyeing top spot, set about compiling a target after claiming a first-innings lead of 63.
Kent were earlier bowled out for 336 with Yasir Arafat finishing with five for 84.
Left-hander James Adams hit a career-best 262no as Hampshire posted 572 for three declared against Nottinghamshire at Trent Bridge.
John Crawley was dismissed for 148 having put on 276 with Adams for the second wicket.
Notts were in deep trouble at the close on 173 for five with Shane Warne and Chris Tremlett having taken two wickets apiece. Captain Stephen Fleming was at unbeaten on 64.