They bowled out the hosts for 217 in their second innings to leave a victory target of 188, and had reached 16 without loss off seven overs by the close.
Northamptonshire snatched a first-innings lead at the halfway mark of their clash with Kent thanks to captain Stephen Peters' century.
Peters enjoyed one mid-afternoon let off, but otherwise maintained intense concentration for 297 minutes to post his first hundred of the summer and help his side reach 303 in reply to Kent's first day total of 271 - a first innings lead of 32.
Murray Goodwin scored his first half-century for Glamorgan to help the Welsh county into a dominant position on the second day against Lancashire at Colwyn Bay.
The former Sussex batsman made 69 as Glamorgan reached 242 all out - a first-innings lead of 119.