However for most of the results counting will not take place until Friday morning.
The Conservatives also had a councillor elected in Paisley's Ferguslie Park - the most deprived part of Scotland - for the first time ever. In fact they are looking forward to it, for two reasons.
The party, it continued, had won "more seats" and "an increased and higher share of the vote" than any other party. That won't be the case at a first past the post general election.
Meanwhile polls have warned that Labour, which won a majority in four councils five years ago, could be facing "heavy losses".
But coverage of the contest there has overlooked a number of factors.
Scottish Labour, a party that used to weigh its vote in town halls across Scotland, particularly in the West, did predictably badly, now finding itself where the Scottish Tories once languished, unloved and increasingly irrelevant. If the local results show there is a genuine Conservative challenge in Moray the SNP will hand Robertson all the resources he needs to see it off.
"And yet they lost the election yesterday".
Davidson claimed the Tories were now poised to take SNP-held seats such as Gordon, the constituency held by Alex Salmond, if the results were replicated on June 8. Stuart Donaldson looks sunk in West Aberdeenshire and Kincardine (WAK).
The council is completed by Independent candidate Duncan Cumming, who was elected in Bearsden North.
Scotland's nationalists failed to gain ground in local-government elections as Prime Minister Theresa May's Conservatives cemented themselves as the biggest threat to their dominance after campaigning against another independence referendum. I don't think it's right to compare this election with 2012.
The Conservatives are hoping they might be able to defeat the Scottish National Party's (SNP) Westminster leader Angus Robertson after winning the most votes in the local council elections in his constituency of Moray.
Speaking at the count in Edinburgh, Ms Davidson said: "I would like to thank everyone yesterday who went out and voted Scottish Conservative".
The SNP will also be keeping a close eye on East Dunbartonshire. The whispers coming out of SNP HQ are that they are anxious.
Ukip leader Paul Nuttall has put the party's dismal showing in the local elections down to it being "the victim of its own success" on Brexit.
Labour MSP Anas Sarwar said losing seats is "disappointing" for the party.
"It speaks volumes. If I was a Tory I'd be very ashamed right now".
But the story of the night was the Tory revival, or rather continuing revival given its surprisingly good performance at last year's Scottish Parliament elections.
Katherine Walker, who had her say via postal vote, said: "I'm not so sure about the paper, about the way they set it out".
On the face of it, there will likely be much for the SNP to celebrate.
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