Three men in their 20s have been arrested after allegedly driving a stolen Mercedes Benz erratically after a series of home invasions in Melbourne's north.

Police secretly followed the sedan for several hours after spotting it about 12.30pm on Wednesday. The car had been seen at aggravated burglaries and the drivers had evaded police over recent days.

The Mercedes was driven erratically on Thursday, police said, crossing onto the wrong side of the road and almost smashing into other cars in the CBD and northern suburbs.

Police said the car was eventually dumped at a shopping centre in Coburg North about 5pm.

The occupants ran to a nearby ute, driven by an accomplice, police said.

Three men in their 20s from Wallan, Pascoe Vale and Lalor were arrested and are assisting police.