Barton, slavishly obedient to the party line, had the tacit backing of Whitby's people.
He was proposed by cabinet member Alan Rudge, who is about as close politically to Whitby as it is possible to be.
But Barton, a pugnacious, old-fashioned, outspoken working class Tory with a love of caravanning, did not win.
In what appears to be a clear message about the need to change, the group opted for IT-savvy, media-friendly Parkin, who has only been a city councillor for six years - which in Tory terms is equivalent to about five minutes.
Parkin, who represents Sutton Trinity, has a rock-solid Conservative seat and is clearly going to be around for some time to come.
Unlike many of his older colleagues, he's into social media and is an enthusiastic user of the micro-blogging Twitter site.
He has also managed, quite cleverly, to distance himself from some of the more unpleasant members of a clique of youngish Birmingham right-wingers, while still appearing to represent something new and fresh.
His success should give Mike Whitby food for thought and all eyes will be on the distribution of Tory cabinet seats and committee chairmanships to be announced at the annual council meeting on May 25.
Rumour has it that Whitby will be forced to make concessions to the supporters of Coun Randal Brew, who unsuccessfully challenged him for the Tory group leadership a year ago.
A cabinet seat for Brew is not an impossibility, perhaps in a new finance role.
But what about Parkin? Surely the deputy leader of the largest political group on the council must be offered something rather more challenging than membership of the regeneration scrutiny committee, which is his only official role at the moment.