The extinction of the dinosaurs 65 million years ago had little effect on the evolution of mammals, according to a study in the journal Nature.
One theory had suggested the rise of the mammals was directly linked to the disappearance of the dinosaurs.
The evidence challenging the connection comes from the most complete family tree compiled for mammals.
It shows how different groups, such as primates and rodents, are related and when they diverged.
An international team compiled the mammal "supertree" from existing fossil data and from genetic analyses.
Throughout the Cretaceous Period, when dinosaurs walked the Earth, mammals were relatively few in number, and were prevented from diversifying and evolving in ecosystems dominated by the ancient reptiles.
According to the established view, the extinction of the dinosaurs removed this constraint, allowing mammals to diversify and flourish, and placing them on course to their present position of dominance on Earth.
Under this model, placental mammals split into major sub-groupings, which originated and rapidly diversified after the mass extinction event - thought to have been caused by an asteroid or comet striking Earth 65 million years ago (a point in time recorded in rocks and referred to by geologists as the K-T boundary).
Co-author Kate Jones, from the Zoological Society of London, told the BBC Radio 4's Leading Edge programme: "The meteor impact that killed off the dinosaurs has traditionally been thought to have given mammals the edge they needed."
However, the supertree shows that the placental mammals had already split into these sub-groups by 93 million years ago, long before the space impact and at a time when dinosaurs still ruled the planet.
After the origin of these sub-groups - or orders - the rate of mammal evolution fell and remained low again until the Eocene Epoch, 55 million years ago.
The start of the Eocene was marked by rapid global warming and an explosion in the diversity of mammal lineages.
"The [supertree] is a new way of showing all the mammal species on the planet, starting with a common ancestor. Species relationships can be inferred from morphological characteristics and genetic sequences," explained Dr Jones.
"If we had done this from scratch, we would have had to get molecular and morphological data for 4,000 different species.
"What we did instead was use already published information from hundreds of researchers around the world. We used a new technique called supertree construction which allows us to get all the information that's out there, re-code it and re-analyse it as if it's all part of one dataset."
'Straw man' theory
The composition of rocks and marine sediments laid down at the boundary between the Palaeocene and Eocene epochs shows that global temperatures rose by around six degrees Celsius in less than 1,000 years - an event known as the thermal maximum.
Dr Rob Asher, an expert on mammalian phylogeny at the University of Cambridge, said: "Palaeontologists have known for over a hundred years that not all modern placental mammal groups appear right after the K-T boundary.
"Most orders of placental mammals - what I mean by that is cats and bats and whales and people - appear at the Eocene. On the flipside, not all dinosaurs disappear at the end of the Cretaceous.
"There was a period of several million years at the end of this period which witnessed several extinctions of non-avian dinosaurs. So the old textbook idea that at the K-T boundary dinosaurs disappeared and mammals appeared is a bit of a straw man."
But the idea that mammal fossils from the Cretaceous represent ones ancestral to today's mammals was a controversial question, said Dr Asher.