Rotherham United 2 Gillingham 0
The home side have missed a hat-trick of matches because of the Arctic weather, but carried on where they left off with a win at the end of January.
A first half effort from Clarke - on loan from Blackburn Rovers - put the home side in front and left-back Green sealed it with his second ever goal.
New boy Clarke had an early taste of action after his weather delayed debut but was off-target with his first effort.
And Reuben Reid, Rotherham's leading scorer, went close but guided his header wide of the mark after a quality cross from Green on the left.
Gillingham, boasting a hat-trick of away wins before their arrival at the Don Valley Stadium, found it difficult to produce any efforts of note and wasted early opportunities that came from corners.
Rotherham struck though midway through the first half to settle their early nerves when Clarke found the mark.
Dale Tonge forged an opening with a clever low ball from the right and after two efforts were blocked Clarke was alert to the opportunity hitting a firm right-foot shot into the open net after Simon Royce was left stranded.
The goal sparked Gillingham into life and as the home side backed off Simeon Jackson rammed a goal bound shot from inside the area but keeper Andy Warrington blocked and Ian Sharps tidied up.
An opportunity opened up for the visitors after 54 minutes when the ball fell to Stuart Lewis 25 yards out, but his ambitious shot screwed well wide and failed to trouble Warrington.
When Gills boss Mark Stimson made a double substitution after 65 minutes it almost paid off immediately.
The ball broke to new arrival Dennis Oli who darted forward and fired a shot from 18 yards that Warrington managed to save with is legs.
And when the Gills won a free-kick outside the area John Nutter caused problems and Nicky Southall's shot from the edge of the area was cleared.
A rare second-half chance came Rotherham's way when Tonge swung in a right-sided cross but Ryan Taylor's header was over.
But on 81 minutes Green broke from just inside the Gills half, raced forward and lashed a super shot out of Royce's reach to kill off the visitors.