Higdon put Stuart McCall's men on the road to victory with a ninth-minute header before midfielder Law struck in the 63rd and 79th minutes to kill off any hopes the Dark Blues had of a comeback.
Dundee remain 13 points adrift at the foot of the table with relegation looming but for Well it rounded off the perfect week after manager McCall had signed a new contract to extend his stay at Fir Park.
Dundee manager John Brown found himself up against old Rangers team-mate McCall who took his on-form Well side to Tayside on the back of a convincing 4-1 win over Hibs in their last outing.
Dundee had an early opportunity after five minutes when Motherwell defender Shaun Hutchinson was dispossessed by winger Nicky Riley.
Riley quickly made his way into the visiting penalty area but his intended cross for John Baird lacked power and swept to safety.
However, the Steelmen surged ahead in the ninth minute.
Chris Humphrey's deep cross from the right took the Dundee defence by surprise as it found its way all the way to the back post.
Higdon was lurking and he rose unchallenged to head past new Dark Blues keeper Steve Simonsen from close range.
Dundee were well aware of the threat posed by James McFadden going into this mach and the Motherwell man brought out a fine diving save from Simonsen after 16 minutes, diving low to his left to parry away the striker's shot.
It was all 'Well and shortly after Humphrey skinned Brian Easton before crossing for Henrik Ojamaa who fired straight into the arms of Simonsen.
Midway through the first-half, Riley was set to run through on goal when Hutchinson brought him down but referee Steven McLean did not deem it to be a last-man challenge so only produced a yellow card.
Dundee's best chance to level came after 29 minutes as Gary Harkins' 20-yard drive was saved by visiting keeper Darren Randolph, and John Baird screwed the rebound just inches past the far post.
Higdon threatened to grab his second of the afternoon just after the restart with a hooked shot from 12 yards which went narrowly over the bar.
But the Steelmen went 2-0 ahead in the 63rd minute.
Keith Lasley's flighted cross from the right was met by the on-rushing Law who flicked a header low into Simonsen's right-hand corner.
That was no more than the visitors deserved and they added another in the 79th minute to complete the rout.
Tom Hateley's corner found Law unmarked on the far edge of the penalty area and the midfielder took a touch before curling his unstoppable effort into the top corner with Simonsen beaten to leave Dundee deflated and staring at the drop back down to the First Division.
- Sports & Recreation
- Steve Simonsen