This is my personal opinion so feel free to rip it apart.

In the movie itself, That was the only thing Sonny did as Don. He became Don and 2 minutes later he is dead. I think the whole point of Sonny's character was to make Michael "that much better of a Don". So, they needed Sonny to "mess up BAD". I think with the car not being able to follow him was just for the fact that Sonny was so pissed off that he was just flooring it and they could never catch up. When you see the other guys pulling up AFTER HE WAS SHOT, that was just to show how fast he was actually going, how hot headed he was. (Then when calm Michael comes in it looks that much better)

Also and this might be a stupid excuse but, what if Sonny's car was just FASTER than the car the other guys were driving?