The pair were the key minds behind a NASA mission to measure the aftershock of the cataclysmic explosion that occurred some 13.7 billion years ago and gave birth to the cosmos.
The unmanned spacecraft, the Cosmic Background Explorer (COBE) satellite, not only gave flesh to the skeletal notion of the "Big Bang" -- which had developed in academic circles in the late 1940s -- but also offered clues as to how and when the first galaxies came into being.
Big Bang breakthrough
The results from COBE were "the greatest discovery of the century, if not all times," the British physicist Stephen Hawking has said.
Dr Mather was lauded for his work on so-called blackbody radiation – a telltale pattern in the energy spectrum which comes from a body that is cooling down.
At its birth, the Universe was 3,000 degrees Celsius. Since then, according to the Big Bang theory, the radiation has gradually cooled as the Universe has expanded.
This so-called cosmic microwave background (CMB) radiation -- the shockwave of energy that issued from the blast and is still radiating across the expanding skies as limits of the Universe are pushed back -- is barely 2.7 degrees above absolute zero, which is minus 273 degrees Celsius.
COBE was launched in November 1989.
The first results were received after nine minutes of observations, providing "a perfect blackbody spectrum," in other words -- as predicted – a temperature profile of the Universe at that point after the Big Bang, the Nobel panel said.
When the curve was later shown at an astronomy conference, the results received a standing ovation.
"There really is not a good alternative explanation for having such a perfect black body spectrum. Many people looked, but no good explanation was found, so the Big Bang theory is confirmed by that spectrum," Dr Mather said.
Professor Smoot's prize was for measuring tiny variations in the temperature of this radiation, thus proving the direction of the force of the Big Bang and the still-continuing expansion of the Universe.
These temperature differences also amount to fingerprints for cosmic sleuths, as they are the thresholds at which the matter in the infant Universe comes together.
The award was a de-facto award for a space mission, the first time this has happened in the history of the Nobel Prize. More than a thousand researchers and engineers worked on the COBE project, which Mather also coordinated.
Lucrative honour
The two laureates will each receive a gold medal and a diploma and will share a cheque for 10 million Swedish kronor ($A1.84 million) at the formal prize ceremony held, as tradition dictates, on December 10, the anniversary of the death in 1896 of the prize's creator Alfred Nobel.
On Monday, the Medicine Prize went to US research duo Andrew Fire and Craig Mello for their discovery of how to silence malfunctioning genes, a breakthrough which could lead to an era of new therapies to reverse crippling diseases.
The prize for chemistry will be announced on tomorrow, to be followed over the next 10 days by the awards for economics, literature and peace.