story identification - "Not with a whimper, but with a roar of triumph!"

Looking for the title of an old sci-fi book, pretty sure it is a Baen or Del Rey imprint. Basically, mankind has reached the stars and expanded throughout the galaxy. Suddenly, an unknown race appears and begins a war of extermination against man. Finally, the galaxy is desolate, and one man remains. He is in a starship with an AI and becomes injured in the battle.

The ship's AI takes over and speeds out into the unknown, followed by the last remaining member of the unknown alien race. As all speeds are at tremendous multiples of the speed of light, the man cannot get away, but the alien cannot catch up.

Finally, communication is opened, at which point the man asks "why?" The alien tells him that man had discovered immortality, but that it required the death of a member of a race known as the Flower People for every human who achieved immortality. The alien says that Man would have found the answer eventually, but that genocide was so intolerable that the aliens came from another dimension, to which they could never return, to stop Man, which resulted in the war of extermination.

Finally, the light speeds become so great that the two remaining living beings in the universe approach the Big Crunch. As the Man begins to dive into the singularity, with the alien hot on his heels, he says that maybe there will be room in the next universe for both races to live in peace, and the final line is "not with a whimper, but with a roar of triumph"!