How credible is the ending of Collateral?

Most people don't understand the ending, and think it's just a traditional Hollywood happy ending, another deus ex machina to give us what we expect.

Very few viewers seem to realize that the ending is not just the final confrontation between Max and Vincent, but between their own philosophy on life itself. Vincent is an extremely well-disciplined hitman but his outlook is fundamentally nihilistic in nature. While he appreciates the spontaneity embodied by the jazz music they discuss, and seems to thrive on adaptability, in the end he loses the gunfight precisely because he's become too set in his patterns (specifically, his rote technique of shooting a Mozambique-type failure drill by firing a double tap into the sternum, and a third shot to the head).

In contrast, Max, the man who has lived the past twelve years of his life in a regimented, automated pattern (visit his mother, keep the cab clean, always look to his photo of the Maldives to calm his nerves, etc), learns via Vincent to break out of his habits and realize his full abilities as a person. Vincent's speeches about improvisation, adaptation, taking risks, and appreciating spontaneity set the stage for Max's transformation, and it's Vincent's threats that force him to take action when Vincent finally starts threatening the people he cares about (his mother, Daniel, Annie, etc). Under stress, Max manages to find himself and succeeds at putting on a performance for Felix, crashes the taxi to wrest control of the situation back away from Vincent, and finally manages to muster the courage to directly confront him in the last few scenes.

Going into the final shootout, these factors are what determined who won, and why. Vincent becomes stuck following his predetermined path of killing Annie, and can't break free of his imperative of finishing the job, even though a hitman as experienced as he should have known to call it off by then. Max has found himself under fire, and once running is no longer an option, realizes he has to finally make a stand. Vincent's penultimate statement "I do this for a living!" reflects the fact that he no longer knows or remembers any other way than what he's doing.

At the moment of gunfire, Vincent attempts to engage Max using the exact same tactic he's used all throughout the film: double tap to the chest followed by a headshot. He sees Max, he aims at Max, he fires...but he's no longer able to process changes or adapt to them, and he fails to register or react to the presence of the steel door frame between them. All three of the shots from his stolen S&W impact the door frame and fail to penetrate (which is fairly realistic). In contrast, we can see Max clearly close his eyes and fire blindly. He's not become some super-skilled gunman, he's simply learned how to let go and act rather than stall, delay, or deny reality. Most of his shots go wild, but one passes through the window and is just good enough to score a vital hit on Vincent. Luck, but luck driven by their respective mental states at the time. Max won because he succeeded at learning from Vincent's philosophy, while Vincent died because he lost track of the same.