The Louisiana Purchase

Jefferson did it constitutionally by negotiating a treaty with Napoleon, ratified by the Senate.

But he thought he was cheating.

Jefferson and others felt that, absent an express grant of power, the federal government could not acquire territory.

However, the federal government was given express and exclusive power to make treaties, and history testifies that the purchase of territory is a perfectly banal use of that power, as are the acquisition of territory through victorious war and the surrender of territory to end a lost one.

So they were mistaken.

On the other hand, when the Congress set about erecting a government for the new territories it exceeded its powers.

The grant of power in Article IV, Section 3 applies to the Northwest Territory and existing US property, and does not appear to contemplate new territories. 

While on the subject of widespread constitutional error, even among officials and even from the beginning, consider this.

Some people, some of them government officials, have believed or claimed to believe, or merely claimed, throughout  much of the life of the Republic, that the judicial power lodged by the constitution in the federal courts contains intrinsically and inherently the power to nullify laws or other acts of government that conflict with the constitution.

History does not support that claim, that I am aware.

Jefferson's outraged incredulity was in that case entirely justified.

IMHO.

Update 12062014.

I now see the treaty power as restricted so that it can commit the government to doing only what the constitution elsewhere empowers it to do.

But I also now read both the first and 18th clauses of Article I, Section 8, as real grants of real powers.