Despite Ireland's first-half dominance, four Greig Laidlaw penalties kicked Scotland to what looked like an improbable victory, following up their comprehensive win over Italy.
But with Wales arriving in Edinburgh also harbouring slim hopes of a Championship win, Blair has issued a warning that Rob Howley's team will not waste the kind of possession Ireland enjoyed.
"I can certainly see us beating Wales", said Blair, who won the last of his 85 caps against South Africa last autumn.
"But things need to change a bit. If you give Wales the amount of territory and possession we did Ireland, then I don't think it's realistic to say we can win back-to-back games in those circumstances.
"From what we showed against England and Italy, if we are able to get a decent stream of possession against Wales and play sensibly, then I think a win is definitely possible.
"There is obviously a huge improvement in terms of the results this year. Winning two games on the trot is a massive positive.
"The way we played against Italy was to absorb the pressure and then hit out on the break. With the squad at the moment we have players capable of scoring 80m tries like Stuart Hogg.
"Where previously we've been able to defend very well, we didn't necessarily have that punch to take our opportunities.
But there are now some exciting guys in the team who have the X factor."
Blair, now playing his rugby for Brive in France, says the win over Ireland in the last round would have left Scott Johnson and his players with more questions than answers about their own game.
Ireland enjoyed 71 per cent possession and 77 per cent territory at Murrayfield but failed to take advantage of their dominance with points on the scoreboard.
But Scotland bagging the win means they still potentially could have all to play for in Paris next weekend if they come away with a victory again this weekend.
"One of the impossible things to put your finger on is how or why you win a game", Blair added.
"Scotland didn't play very well against Ireland. They defended well in parts and scrambled well and showed real desire.
"We didn't even get the rub of the green with Ryan Grant's sin binning. But it just a gutsy display.
"And off the back of the display against Italy it puts us in a great position in the championship."