Wales, seeking a seventh successive victory over the Scots, were leading 10-3 after a Liam Williams try when Scotland fullback Stuart Hogg was red carded for a dangerous late charge on Dan Biggar in the 22nd minute.
Wales took full advantage with two tries each for George North and Jamie Roberts and one each for Toby Faletau and Rhodri Williams as they easily surpassed their previous record winning margin in any Five or Six Nations game - the 39 points by which they beat Italy in a 47-8 triumph in 2008.
It was also Wales's highest score, overtaking their 49-14 win in France's first championship match in 1910.
Their previous best against Scotland was a 46-22 win in 2005 which was blown away on a day to forgot for losing coach Scott Johnson, who had already announced he would move into a director of rugby role with the national team after Saturday's match.
The Welsh had gone into the championship hoping for an unprecedented third successive outright title but will finish third or fourth with six points from three wins.
Scotland, whose only victory came against Italy but who were desperately unlucky to lost to France last week, finish fifth on two points. Italy ended up bottom without a win for the first time since 2009.
"It has been a tough few weeks for us," North said in a pitchside interview.
"We went to Twickenham and didn't get the result we wanted against England. We trained really hard after that and I think it showed. I am happy with two tries but all the boys played exceptionally well.
"It doesn't make up for the England defeat, but the performance was good and we finish the campaign on a high note."
FANS HAPPY
A year ago Wales thrashed England 30-3 to take the title in the final match and, though there was a different atmosphere in the Millennium Stadium on Saturday, the fans were given plenty to keep them happy as they left to fill the pubs and bars.
They will, however, look back on the match with a mental asterisk as Hogg's sending-off turned the game into something of a no-contest.
He charged Biggar late, with his shoulder smashing into the flyhalf's face and after initially being shown a yellow card, the referee then flourished a red, seemingly after seeing a replay of the incident on the big screen.
Biggar was lucky to escape serious injury and carried on as Wales soon took command. Williams, who delivered a man of the match display in place of the injured Leigh Halfpenny, set up the second try with a great break, finished by North.
Roberts completed another impressive move with his first try, and with Biggar converting all three, and landing two penalties, Wales led 27-3 at the break.
There was no let-up in the second half as within a minute of the restart more good hands sent North over in the left-hand corner.
Roberts got his second after a wonderful length-of-the field move by Wales following an overthrown lineout and, with Scotland's tackling falling apart, Faletau helped himself to another as Wales led 44-3 after 53 minutes.
That meant they had scored more tries in an hour than they had managed in four previous Six Nations games.
The usual avalanche of replacements took the momentum out of the Wales attack for a while but the Welsh, for whom prop Gethin Jenkins was making a national record 105th appearance, found their second wind and rounded off a satisfying afternoon with another well-worked try by Rhodri Williams.
The title they won in 2012 and 2013 will now be handed over to England or Ireland later on Saturday.
Earlier, England beat Italy 52-11, while France host Ireland later in the final game of the championship. An Irish victory would give them the title and any other result would leave England as champions.
