Dundee boss Jim Duffy hands another Dens Park youngster a debut, with Douglas Cameron claiming a place in the starting 11 as the Dark Blues struggle with injuries.
Dundee captain Barry Smith fired just wide from outside the area with six minutes played.
Five minutes later, Julian Speroni was called into action twice in a matter of seconds when he was forced into saves to deny Derek Adams and Keith Lasley.
Midway through the half, Dundee defender Dave Mackay fired high and wide of the target from 25 yards.
Moments later, Fabrizio Ravanelli should have hit the target, but from five yards he headed Garry Brady's free-kick over the crossbar.
Seven minutes after the interval, Motherwell went ahead when Steven Craig met David Clarkson's low cross on the run to sweep a low right-foot shot across Speroni and into the corner of the net.
Debut boy Cameron cracked a 25-yard left-foot effort inches over the crossbar a minute later.
Lasley saw his long-range effort go just past the upright with a quarter of the match remaining.
Despite seeing plenty of the ball, the home team had their first shot on target with 68 minutes played when Ravanelli's 18-yard shot was saved by Gordon Marshall.
Dundee boss Jim Duffy was forced to push Juan Sara into what was now a four-man attack as his team went in search of an equaliser.
Three minutes from time, it was the visitors who almost scored again but Alex Burns' low drive went inches past the post.
Another goal wasn't needed as Motherwell held on in the dying minutes to claim another three points which moves them above Dundee and into fourth place in the SPL.