South African star Kleinveldt smashed a superb 91 from just 88 balls as David Ripley’s men eventually made it to 321 before being bowled out in 86.4 overs.
Saif Zaib was also in the runs, securing a maiden first-class half-century before finishing unbeaten on 65 from 113 deliveries.
Laurie Evans was another man to make it past the half-century mark as the Warwickshire loanee registered an impressive 74 on his debut.
Northants then started brilliantly with the ball, with Ben Sanderson grabbing two wickets in an over.
Most Popular
-
1
Super Zaib helps Steelbacks to chase down Eagles
-
2
Saints players can show what they are made of during hectic start to season
-
3
Northamptonshire share spoils with Warwickshire after 'turgid' final day
-
4
NORTHANTS CRICKET LEAGUE: All your results and fixtures
-
5
Ripley admits Northants will 'have to do it the hard way' as they bid to save game at Lancashire
Muhammad Azharullah went one better as he claimed three scalps, with Glamorgan limping to 139 for five ahead of the third day.