Actually, your last paragraph is more the case than not.
There are currently three common definitions for delineating discrete species:
1) Phenotypically different from related species (looks or acts differently).
2) Produces viable offspring in the wild.
3) Some % of genetic difference.
There are strengths to all three:
1) Very easy to ascertain and measure.
2) Most common conception of a species.
3) Genes control the first two, so genetic divergence gets to the heart of the matter.
There are also weaknesses to all three:
1) Is notorious for mis-labeling and missing species.
2) Some species which can mate and produce fertile offspring under enclosed conditions do not do so in the wild (Tigers and Lions, for instance).
3) The amount of divergence has, thus far, been completely arbitrary. If there is a certain % or patterns of mutation required in the genome, science hasn't yet discovered it.
The fuzzy definition of species, combined in the not-exactly-intuitive generational-type thinking required for understanding evolution, and the answer to your question is (at least to the best of my understanding) the following:
Yes, at some point one of our ancestors gave birth to the first Homo sapien that was somehow genetically different from its parents. However, the magnitude of the difference is probably not as great as you might think.
We've already observed our closest evolutionary cousins, the Bonobos, making basic tools through flint napping: http://www.newscientist.com/article/dn22197-bonobo-genius-makes-stone-tools-like-early-humans-did.html
It's also possible that disputes between male chimpanzees are mediated by an older female: http://www.cpradr.org/Resources/ALLCPRArticles/tabid/265/ID/121/Primates-and-Me-Web.aspx
And that both Chimpanzees and Capuchin monkeys can be taught the concept of currency (which, somewhat comedically, they then used for prostitution): http://www.nytimes.com/2005/06/05/magazine/05FREAK.html?ei=5090&en=af2d9755a2c32ba8&ex=1275624000&partner=rssuserland&emc=rss&adxnnlx=1118160068-1EGJuan4FJH1LooxHYd5/g&pagewanted=all
Then there's the everlasting impact of Koko, the Silverback Gorilla who was taught - and perfectly capable of replying in - sign language: http://en.wikipedia.org/wiki/Koko_%28gorilla%29
The idea that humans jumped onto the scene with unforeseen amounts of intelligence and capability probably isn't what happened. Obviously we are capable of constructing and using the most advanced tools on the planet, but this is after several thousand generations of innovation. The very first human might have been more intelligent (or at least had the capacity to be), but otherwise probably fit in pretty well with its parents and other relatives since the vast majority of what we learn comes from our parents and personal experience.
Then over time the number of individuals with the capacity for higher modes of thinking increased as a result of the genetic inheritance of whatever mutation created the first human. The first human, to put it simply, was successfully able to pass on their mutation which gave them our unique traits, and their offspring were also successful - until you have an entire population of humans living amongst each other. Eventually our innovative capacity lead, step by step, to our dominant position on the planet.
Even now humans are yet evolving. Lactose tolerance (the ability to consume dairy products after childhood) is a very new trait among humans (and unprecedented among all mammals) only a few hundred generations old (roughly 10,000 years) that evolved twice in separate populations of humans (North Africa and Northern Europe). Our jaws are getting progressively smaller (which is why some people have to remove their wisdom teeth to maintain a straight smile - and some people don't have wisdom teeth at all), some muscles are disappearing (the Palmaris Longus is one example - it's present in about 80% of humans), and other subtle changes are occurring.
Just don't make the mistake of equating "evolved" with "superior." Evolution is dictated by the ever-changing demands of the environments we find ourselves in, and what's beneficial today isn't guaranteed to be beneficial forever.