Pole-sitter Ryan Hunter-Reay led from start to finish to claim victory ahead of the Kiwi while Will Power was third.
"This is so awesome," Dixon said. "You always doubt these situations that it is going to happen."
"It is all about the people. I am the lucky one that gets to take it across the line.
"This doesn't come without a lot of hard work. We had a lot of things that could have gone wrong today.
"Rossi did a hell of a job. He pushed hard this year he is a real talent and has a big future ahead of him.
"We were just making sure we didn't get ourselves into an awkward moment that they could capitalize."
Dixon joins only the great AJ Foyt as a five-time series champion.
Rossi was naturally disappointed that basically any chance he had of winning the title ended on the opening lap and he wasn't sure what actually happened.
"I don't know," he said. "I got a good start – I don't know if [Andretti] lifted or I misjudged it. I don't know if I would have been able to catch Scott anyway.
"The team did a great job to get me back on the road to recovery after the mistake I made.
"A huge congrats to Scott – he is a five times champion for a reason and he is a great guy to race."