Murphy came within inches of getting a third in the space of six minutes soon after when he cut inside before firing in a powerful effort that clipped the crossbar.
Murphy continued to threaten and was only denied from netting his second of the game by a fine save from Antonio Reguero.
The visitors put the game well and truly beyond doubt with just under 20 minutes left when Law found Henrik Ojamaa, who proceeded to put the ball through the keeper's legs to make it 4-1.
Inverness almost came up with an immediate response, but Aaron Doran's long range effort was tipped onto the crossbar by Randolph.
The away side put the icing on the cake in the 89th minute as sub Omar Daley sent a dipping shot straight at Reguero, but the keeper let it go right through him and into the net.
The result, Inverness's first defeat since their last encounter with Motherwell, leaves the hosts sixth in the table, while Motherwell leapfrog them into fourth.