The SNP's plan to keep universities fee-free for Scots but charge students from elsewhere is also "legally unsustainable", the Better Together leader said in an address at St Andrews University.
New powers for Scotland are "guaranteed" if it votes No but the extent of these powers will be subject to the approval of UK voters in the general election, he said.
Independence risks the free movement of trade and people across the border, he added.
He also attacked the "childish fairy story" espoused by "romantic nationalists" that Scotland's identity has been absorbed by its larger neighbour.
"It's perfectly plain that their idea of free university education for Scots, but charging students from elsewhere in the UK, is legally unsustainable, and their assertion that Research Council funding would remain even after Scotland had left the UK is simply laughable," he said.
He added: "Each of the three main political parties now has detailed proposals to extend the Scottish Parliament's tax powers, and to extend its powers in other areas as well.
"Of course these will have to be presented to the people in a general election, but all the parties are guaranteeing to legislate after that election.
"Following the general election next spring, we can have confidence those promises will be delivered."
He continued: "The union may have merged parliaments, but it never did merge Scotland into England. Instead Scotland retained its own institutions which over decades and centuries continued to develop."
He cited the growing influence of the Scotland Office in the late 20th century and the foundation of the Scottish Parliament.
"When we understand the history properly it gives the lie to the alternative, romantic, nationalist narrative, a fable about how our small nation was absorbed by a larger neighbour and struggled to regain its identity through the efforts of a small band of patriots. This is no more than a childish fairy story," he said.
"Scotland has been part of a deep economic union for so long we take it for granted. It's actually quite hard to imagine a world in which Scots could not move with complete freedom to take up jobs elsewhere in the UK.
"We assume without question that Scottish businesses can buy and sell in a market so open that the border between Scotland and England does not matter in the slightest to trade.
"We take for granted that businesses can secure capital to expand from any financial institution in the UK, regardless of the effect of the border.
"At this point nationalists usually say that independence will change nothing in the economy, and that trade will continue unaffected.
"They sometimes refer to the European single market.
"This is to misunderstand the nature of international borders. All the evidence is that international borders affect trade."