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.
Inverness kept up their pursuit of European football with a 2-1 win at Hibernian.
Second-half goals from Ross Draper and Andrew Shinnie, either side of Leigh Griffiths' 23rd goal of the season, were enough to earn them the victory, keeping them three points behind Motherwell in second and extending their lead over Ross County in fourth to five points.
For Hibernian the result spoiled the return to the club of Scotland international Kevin Thomson and leaves the club languishing in eighth place, having won only one of their last nine league games at Easter Road.
Niall McGinn ended Aberdeen's long wait for a goal against Hearts and kept their top-six hopes alive as his double gave Craig Brown a 2-0 victory in his final home match as manager.
McGinn netted 10 minutes into each half in front of 10,175 fans at Pittodrie to keep them in the race for the top half ahead of their trip to Dundee United next Saturday, after which the SPL splits in two and Brown steps down.
Brown's replacement, Derek McInnes, would have been impressed with Aberdeen's attacking play as he watched from the stand with wide men McGinn and Jonny Hayes causing problems for a fragile-looking Hearts defence.
James Fowler's second-minute goal was enough to secure a 1-0 victory for Kilmarnock at Ross County.
It was only County's third SPL defeat of the season at Global Energy Stadium but one they should never have lost having dominated most of the match.
But they were no the back foot almost from the off as Killie got off to a flyer with an early goal. Jereon Tesselaar swung a cross in from the left and Rory McKenzie's lay-off was swept high into the net by Fowler.
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