Winger Jacob Stockdale, in only his eighth game for Ireland, bagged a brace of tries to take his overall global tally to 10, while further scores from Conor Murray and Sean Cronin handed a ruthless Ireland a thumping win.
They can clinch the title later if defending champions England - who the Irish play next Saturday at Twickenham - fail to secure a bonus-point win over France in Paris.
"If the game loves us then we might have won against France, but we didn't get bounce of ball, we didn't get the 50/50 decisions and we are in the losers' chair and it is not a very happy place".
"It's special because we won it at home", Schmidt said.
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Two tries by Jacob Stockdale set up Ireland's dominant 28-8 victory over Scotland on Saturday which a few hours later proved to be enough for them to clinch the Six Nations title.
"We need to make sure that when we have these experiences that are tough, it goes into our work to improve".
"It's been in the back of our minds and it's something you always dream of", Murray said of the possibility of emulating the 1948 and 2009 feats.
Scotland showed glimpses of the form that saw them beat England in the previous round of matches but left too many points out on the field through bungled passing.
Sexton's displeasure didn't distract Greig Laidlaw who slotted over the penalty to give them a 3-0 lead.
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Centre Peter Horne's pass was careless and Stockdale intercepted before scorching across the acres of empty turf to score under the posts with Johnny Sexton converting.
Sexton's conversion opened up a 7-3 lead after 24 minutes but Scotland should have been back in front soon after when Huw Jones fluffed his lines by misplacing a pass to Stuart Hogg with the full-back virtually guaranteed to touch down if the delivery was better.
As the odd loose pass crept into the Irish game, Scotland demonstrated the extent of their handling skills in a bright period of play for Gregor Townsend's men.
He's determined he doesn't squander this rare shot at a Grand Slam.
"They are a very good team", added the backrow. We probably had four chances, three clean two on one chances and we took one so.to me that's the difference. They have fought out incredibly tough finishes.
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Scotland got some reward for their efforts when Blair Kinghorn scored his first worldwide try in the corner after a good spell for his side.