Newby produced the perfect trio as the Shrimps stormed into a 4-1 half-time lead against a shell-shocked Rotherham side.
There was some sympathy for the Millers, who were recently forced to go into administration, but there were few excuses for their shocking performance in the first period.
There were early warning signs as Wayne Curtis missed two chances to give Morecambe the lead in the first two minutes of the game, heading over from six yards and volleying wide when he had more time.
But those warnings went ignored as Matty Blinkhorn was unmarked in the box to head Morecambe into a seventh minute lead from Garry Thompson's pinpoint cross.
The Rotherham defence were caught out again in Morecambe's next move. Newby looked offside as he latched on to a long through ball, but there was no flag and the striker slid the ball past Warrington with a shot that went in off the right-hand post.
There was more pain to come for the Millers' defence as they failed to cut out another long ball from Thompson and presented Newby with another opening on 18 minutes.
This time he took the ball in his stride and beat Warrington with a smart left-foot finish which ended up in the bottom left-hand corner of the goal.
The shell-shocked Millers finally found their feet and began to cause problems themselves, with striker Derek Holmes heading wide after beating Morecambe keeper Scott Davies to a high ball and Danny Harrison curling an effort over the bar from the edge of the area as the home defence failed to clear their lines.
The pressure paid off when Mark Hudson gave Rotherham a glimmer of hope with a fine finish ten minutes from the break as he beat a flat-footed Davies with a perfectly placed shot from the edge of the area.
Unfortunately for boss Mark Robins the comeback hopes were dashed as Newby clinched the match ball with another quality finish on 42 minutes. Thompson was the provider again as he beat the struggling Jamie Green for pace and his cross was headed past Warrington from 12 yards out.
It was pretty much one-way traffic now, with Blinkhorn denied a second from Newby's right-wing cross by the post and the scoreline would have looked much worse had it not been for keeper Warrington.
The former Doncaster stopper made a superb double save at the start of the second period to block from Curtis and then Thompson's follow-up, before denying Curtis on two more occasions with excellent saves.
But he was beaten once more when with 18 minutes to go former Rotherham defender David Artell knocked down for Craig Stanley to drill a right-footed volley into the bottom right-hand corner to seal a memorable win for the home side.